Jee 2014 Booklet2 Hwt Dynamics of a Particle
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Vidyamandir Classes
DATE :
IITJEE :
NAME :
MARKS : 10
TIME : 25 MINUTES
TEST CODE : DNP [1]
ROLL NO.
START TIME :
STUDENT’S SIGNATURE :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
A 60 kg man pushes a 40 kg man by a force of 60 N. The 40 kg man has pushed the other man with a force of : (A) 40N (B) 0 N (C) 60 N (D) 20 N
2.
Action and reaction (A) act on two different objects (B) have equal magnitude (C) have opposite directions (D) have resultant zero
3.
A body of weight w1 is suspended from the ceiling of a room through a chain of weight w2. The ceiling pulls the chain by a force (A) w1 (B) w2 w1 w2 (C) w1 + w2 (D) 2 When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by (A) the cart on the horse (B) the ground on the horse (C) the ground on the cart (D) the horse on the ground
4.
5.
6.
(C)
y F .y x
VMC/Dynamics of a Particle
(B)
F .y y x
(D)
F .y y
8.
If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be : (A) going up with increasing speed (B) going down with increasing speed (C) going up with uniform speed (D) going down with uniform speed
9.
A scooter starting from rest moves with a constant acceleration for a time t1 , then with a constant velocity for the next t3 to come to rest. A 500N man sitting on the scooter behind the driver manage to stay at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is : (A) 500 N throughout the journey (B) Less than 500 N throughout the journey (C) More than 500 N throughout the journey (D) >500 N for time t1 & t3 and 500N for t2
10.
A horizontal rope of length y is pulled by a constant horizontal force F. what is the tension at a distance x from the end where the force applied ?
F y x
In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle’s motion. A particle of mass m projected upward takes a time t1 in reaching the maximum height and t2 in the return journey to the original point. Then : (A) t1 < t2 (B) t1 > t2 (C) t1 = t2 (D) the relation between t1 and t2 depends on the mass of the particle
for the next t2 and finally with a constant deceleration
A block of mass 10 kg is suspended through two light spring balances as shown in figure. (A) Both the scales will read 10 kg (B) Both the scales will read 5 kg (C) The upper scale will read 10 kg and the lower zero (D) The readings may be anything but their sum will be 10 kg
(A)
7.
59
Consider the situation shown in figure. The wall is smooth but the surfaces of A and B in constant are rough. The friction on B due to A in equilibrium : (A)
is upward
(B)
is downward
(C)
is zero
(D)
the system cannot remain in equilibrium
A
B
F
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [2]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Suppose all the surfaces in the previous problem are rough. The direction of friction on B due to A. (A) is upward (B) is downward (C) is zero (D) depends on the masses of A and B
2.
In order to stop a car in shortest distance on a horizontal road, one should : (A) apply the brakes very hard so that the wheels stop rotating (B) apply the brakes hard enough to just prevent slipping (C) pump the brakes (press and release) (D) shut the engine off and not apply brakes
3.
A block A kept on an inclined surface just begins to slide if the inclination is 30 . The block is replaced by another block B and it is found that it just begins to slide if the inclination is 40 . (A) mass of A > mass of B (B) mass of A < mass of B (C) mass of A = mass of B (D) all the three are possible
4.
Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional forces on the vehicle by the road (A) is towards east if the vehicle is accelerating (B) is zero if the vehicle is moving with a uniform velocity (C) must be towards east (D) must be towards west
5.
Two cars having masses m1 and m2 move in circles of radii r1 and r2 respectively. If they complete the circle in equal time, the ratio of their angular speed 1 / 2 is : (A)
6.
7.
8.
m1/m2
(B)
r1/r2
m1r1/m2r2
(C)
(D)
1
A block is given certain upward velocity along the incline of elevation . The time of ascent to upper point was found to be half the time of descent to initial point. The co-efficient of friction between block and incline is : (A) (B) (C) (D) 0.5 tan 0.3 tan 0.6 tan 0.2 tan Water in a bucket is whirled in a vertical circle with a string attached to it. The water does not fall down even when the bucket is inverted at the top of its path. We conclude that in this position. mv 2 r
(A)
mg
(C)
mg is not greater than
mv 2 r
(B)
mg is greater than
mv 2 r
(D)
mg is not less than
mv 2 r
A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will move (A) towards the centre (B) away from the centre (C) along a tangent (D) will stop
VMC/Dynamics of a Particle
60
HWT/Physics
Vidyamandir Classes 9.
A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the over bridge, the normal force on it (A) increases (B) decreases (C) remains the same (D) fluctuates
10.
A car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a. (A) The acceleration of the car is towards the centre of the path mv 2 r
(B)
The magnitude of the frictional force on the car is greater than
(C)
The friction coefficient between the ground and the car is not less than a/g
(D)
The friction coefficient between the ground and the car is tan 1
VMC/Dynamics of a Particle
61
v2 rg
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [3]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
A person applies a constant force F on a particle of mass m and finds that the particle moves in a circle of radius r with a uniform speed v as seen from an inertial frame of reference. (A) This is not possible (B) There are other forces on the particle
(C) (D) 2.
mv 2 towards the centre r The resultant of the other forces varies in magnitude as well as in direction
The resultant of the other forces is
In the arrangement shown in figure, pulleys are massless and frictionless and threads are inextensible. The Block of mass m1 will remain at rest, if : (A)
1 1 1 m1 m2 m3
(B)
m1 m2 m3
(C)
4 1 1 m1 m2 m3
(D)
1 2 3 m3 m2 m1 m1 m2
3.
m3
A man slides down a light rope whose breaking strength is time his weight ( 1 ). What should be his maximum acceleration so that the rope just breaks ? (A)
g
(B)
g 1
g 1
(C)
(D)
g 2
4.
A particle of a small mass m is joined to a very heavy body by a light strings passing over a light pulley fixed to the ceiling. Both bodies are free to move. The total downward force on the pulley is (approximately): (A) mg (B) 2 mg (C) 4 mg (D) mg
5.
A uniform chain of mass m hangs from a light pulley, with unequal length of the chain hanging from the two sides of the pulley. The force exerted by the moving chain on the pulley is : (A) mg (B) > mg (C) < mg (D) Either (B) or (C) depending on the acceleration of the chain.
6.
A block of mass m is placed over a rough horizontal surface find minimum force required to slide the block on the surface it is given coefficient of friction between block and ground is : (A)
7.
mg
(B)
mg
mg 2
(C)
1 2
(D)
mg 2
A flexible chain of mass m hangs between two fixed points A and B at the same level. The inclination of the chain with the horizontal at the two points of support is . The tension at the mid point of the chain is: (A) (C)
mg tan zero
VMC/Dynamics of a Particle
(B) (D)
mg 2 tan
sin mg
A
B
cos
P
2
62
HWT/Physics
Vidyamandir Classes 8.
A particle of mass 70g, moving at 50 cm/s, is acted upon by a variable force opposite to its direction of motion. The force F is shown as a function of time t. 10 F(N) O
(A) (B) (C) (D) 9.
10.
4 × 10 3 t (s)
8 103 102
Its speed will be 50 cm/s after the force stops acting Its direction of motion will reverse Its average acceleration will be 1m/s2 during the interval in which the force acts Its average acceleration will be 10m/s2 during the interval in which the force acts
Two blocks of 4 kg and 6 kg are attached by springs, they are hanging in vertical position, lower spring breaks due to excessive force. Acceleration of 4 kg block just after breaking: (A) 15 m/s2 (B) 25 m/s2 (C) 10 m/s2 (D) Zero
k = 200 N/m 4 kg k = 100 N/m 6 kg
In the figure, the blocks A, B and C of mass m each have accelerations a1, a2 and a3 respectively. F1 and F2 are external forces of magnitudes 2mg and mg respectively. (A) a1 a2 a3 (B)
a1 a3 a2
(C)
a1 a2 a2 a3
(D)
a1 a2 a2 a3
m
m
m
C
B
A F1 = 2mg
2m
m
D
F2 = mg
VMC/Dynamics of a Particle
63
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [4]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Two objects A and B thrown upward simultaneously with the same speed. The mass of A is greater than the mass of B. Suppose the air exerts a constant and equal force of resistance on the two bodies. (A) The two bodies will reach the same height (B) A will go higher than B (C) B will go higher than A (D) Any of the above the objects are thrown
2.
For the arrangement shown in figure, the tension in the string is given by : (A) (C)
3.
mg 2 mg
(B) (D)
3 mg 2 2mg
2m 30
m
4.
A force F1 accelerates a particle from rest to a velocity v. Another force F2 decelerates the same particle from v to rest, then : (A) F1 is always equal to F2 (B) F2 is greater than F1 (C) F2 may be smaller than, greater than or equal to F1 (D) F2 cannot be equal to F1 5 kg T1 T2 In the figure shown, the table is smooth. Find the ratio of tensions in the right and left strings. (A) 17 : 24 (B) 34 : 12 (C) 2:3 (D) 14 : 13 15 kg 30 kg
5.
A block rests on rough inclined plane making an angle of 30 with horizontal. The coefficient of static friction between the block and inclined plane is 0.8. If the frictional force on the block is 10 N, the mass of the block in kg is (g = 10 m/s2) (A) 2.0 (B) 4.0 (C) 1.6 (D) 2.5
6.
A body takes times t to reach bottom of an inclined plane of angle with the horizontal. If the plane is made rough, time taken now is 2 t. The coefficient of friction of the rough surface is : 3 2 1 1 tan tan tan tan (A) (B) (C) (D) 4 3 4 2
7.
A ladder of length 5 m is placed against a smooth wall as shown in figure. The coefficient of friction is between ladder and ground. What is the minimum value of , if the
A
ladder is not to slip ?
8.
(A)
1 2
(B)
1 4
(C)
3 8
(D)
5 8
O
AB = 5m AO = 4m OB = 3m
B
1 A heavy body of mass 25 kg is to be dragged along a horizontal plane .The least force required is : 3 (A) 25 kgf (B) 2.5 kgf (C) 12.5 kgf (D) 6.25 kgf
VMC/Dynamics of a Particle
64
HWT/Physics
Vidyamandir Classes 9.
A body of mass 10 kg lies on a rough inclined plane of inclination sin horizontal. When the force of 30 N is applied on the block is nearly along. (A) OA (B) OB (C) OC (D) OD
10.
1 3
5 with the
A
30N
B C
O
D
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that : (A) Its velocity is constant (B) Its acceleration is constant (C) Its kinetic energy is constant (D) It moves in a circular path
VMC/Dynamics of a Particle
65
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [5]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Consider the situation shown in figure. The wall is smooth but the surfaces of A and B in correct are rough. The friction on B due to A in equilibrium: (A) Is upward (B) Is downward (C) Is zero (D) The system cannot remain in equilibrium
A
B
F
2.
Two objects A and B are shown upward simultaneously with the same speed. The mass of A is greater than the mass of B. Suppose the air exerts a constant and equal force of resistance on the two bodies: (A) The two bodies will reach the same height (B) A will go higher that B (C) B will go higher than A (D) Any of the above three any may happen depending on the speed with which the objects are thrown
3.
In the balance machine, shown in the figure which arm will move downward ? (A) Left (B) Right (C) None (D) Cannot be said
L/2
L/2
3m m 2m
4.
In the figure, the blocks A, B and C of mass m each have acceleration a1, a2 and a3 respectively. F1 and F2 are external forces of magnitude 2 mg and mg respectively: (A)
a1 = a2 = a3
(B)
a1 > a3 > a2
(C)
a1 = a2, a2 > a3
(D) 5.
6.
7.
a1 > a2, a2 = a3
Essential characteristic of equilibrium is: (A) Momentum equal zero (C) K.E. equals zero
m
m
m
A
B V
C
F1 = 2mg (B) (D)
m
2m F2 = mg
Acceleration equals zero Velocity equals zero
C (m1) A car C of mass m1, rests on a plank of mass m2. The plank rests on a smooth floor. The string and pulley are ideal. The car starts and moves towards the pulley with certain acceleration: P (m2) (A) If m1 > m2, the string will remain under tension (B) If m1 < m2, the string will become slack (C) If m1 = m2, the string will have no tension, and C and P will have accelerations of equal magnitudes (D) C and P will have accelerations of equal magnitude if m1 m2 Two blocks A and B, attached to each other by a massless spring, are kept on a rough horizontal surface 0.1 and pulled by a force F = 200 N as show in the figure. If at some instant, the 10 kg mass has acceleration of 12 m/s2, what is the acceleration of 20 kg mass ? A B (A) 2.5 m/s2 (B) 4.0 m/s2 F = 200N 2 10 kg 20 kg (C) 3.6 m/s (D) 1.2 m/s2 0.1
VMC/Dynamics of a Particle
66
HWT/Physics
Vidyamandir Classes 8.
A cart of mass M has a block of mass m in contact with it is shown in the figure. The coefficient of friction between the block and the cart is . What is the minimum acceleration of the cart so that block m does not fall ? (A)
g
(B)
g/
(C)
/g
(D)
M g / m
a
M
m
9.
A body of mass m is kept stationary on a rough inclined plane of angle of inclination . The magnitude of force acting on the body by the inclined plane is equal to : (A) mg (B) (C) (D) None of these mg sin mg cos
10.
In the system of pulleys shown what should be the value of m1 such that 100 gm remains at ret: (A) 180 gm (B)
160 gm
(C)
100 gm
(D)
200 gm
P1 m1 P2 200gm 100gm
VMC/Dynamics of a Particle
67
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [6]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
A ball weighing 10 gm hits a hard surface vertically with a speed of 5 m/s and rebounds with the same speed. The ball remains in contact with the surface for (0.01) sec. The average force exerted by the surface on the ball is : (A) 100 N (B) 10 N (C) 1N (D) 150 N
2.
The pulley in the diagram are all smooth and light. The acceleration of A is a upwards and the acceleration of C is f downwards. The acceleration of B is : (A) (C)
1 f a up 2
(B)
1 a f up 2
(D)
1 a f down 2
C
A
1 a f up 2
B 3.
4.
5.
6.
W' = 40N
The system shown is just on he verge of slipping. The co-efficient of static friction between the block and the table top is : (A)
0.5
(B)
0.95
(C)
0.15
(D)
0.35
30
W = 8N
Block M slides down on frictionless incline as shown. The minimum friction coefficient so that m does not slide with respect to M would be________: 1 1 3 (A) (B) (C) (D) None of these 4 2 4
m M 37
Neglecting friction and mass of pulley, what is the acceleration of mass B ? (A)
g/3
(B)
5g/2
(C)
2g/3
(D)
2g/5
7 A B 3
If block A starts from rest at t = 0 & begins to move towards right with 2 m/s2 and simultaneously C move towards right with constant velocity of 4 m/s. Velocity of block B at t = 5 sec. will be : (A) 2 m/s C A (B) 3 m/s (C) 4 m/s (D) None of these B
VMC/Dynamics of a Particle
68
HWT/Physics
Vidyamandir Classes A block of unknown mass is at rest on a rough, horizontal surface. A force F is applied to the block. The graph in the figure shows the acceleration of the block with respect to the applied force. The mass of the block is:
8.
(A)
1.0 kg
(B)
2.5 kg
(C)
2.0 kg
(D)
0.2 kg
For what value of M will the masses be in equilibrium. Masses are placed on fixed wedge: (A) 5 kg (B) 4 kg (C) 3.75 kg (D) 3 kg
Acceleration (ms–2)
7.
7 6 5 4 3 2 1 0
5kg
2
4 6 8 10 Applied force F (N)
12
14
M
37
53
9.
Minimum force required to keep a block of mass 1 kg at rest against a rough vertical wall is P. If a force P/2 is applied then the acceleration of the block will be: 0 .5 (A) 5 m/s2 (B) 2.5 m/s2 1 kg P (C) 2 m/s2 (D) 0.9 m/s2
10.
A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The co-efficient of static and kinetic friction are 0.5 and 0.4 respectively. The acceleration of the body is : (A) 6 m/s2 (B) 1 m/s2 (C) 2.5 m/s2 (D) 3.8 m/s2
VMC/Dynamics of a Particle
69
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [7]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
A 20 kg monkey slides down a vertical rope with a constant acceleration of 7 ms 2 . If g 10 m / s 2 , what is the tension in the rope ? (A)
140 N
(B)
100 N
(C)
60 N
(D)
30 N
2.
A block of mass 2 kg rests on another block mass 8 kg which rests on a horizontal floor. The coefficient of friction between A and B is 0.2 while that between B and floor is 0.5. When horizontal force of 25 N is applied on the block B, the force of friction between A and B is : (A) Zero (B) 3.9 N (C) 5.0 N (D) 49 N
3.
Three weights are hanging over a smooth fixed pulley as shown in the figure. What is he tension in the string connecting weights B and C ? (A)
g
(B)
g/9
(C)
8g/9
(D)
10g/9
3kg B A 5kg 1kg C
4.
Figure shows a wooden block on a horizontal plane at a rest being acted upon by three forces : F1 = 10 N, F2 = 2N and friction. If F1 is removed the resultant force acting on the block will be : (A) 2 N towards left F2 F1 (B) 2 N towards right (C) 0N (D) Cannot be determined
5.
A block of mass 2 kg is given a push horizontal and then the block starts sliding over a horizontal plane. The graph shows the velocity time graph of the motion. The co-efficient of sliding friction between the plane and the block is : (A) 0.02 (B) 0.2 (C) 0.04 (D) 0.4
6.
V in m/s
8
O
t in sec
4
The tangential acceleration of a particle in a circular motion of radius 2 m is at t m / s 2 (where is a constant) Initially the particle as rest. Total acceleration of the particle makes 45 with the radial acceleration after 2 sec. The value of constant is : (A)
7.
1 m / s2 2
(B)
1 m/s3
2 m/s3
(C)
What should be the maximum value of M so that the 4 kg block does not slip over the 5 kg block: (A) 12 kg (B) 8 kg (C) 10 kg (D) 6 kg
VMC/Dynamics of a Particle
70
(D)
Data are insufficient
4 kg 0.4 5 kg
M
HWT/Physics
Vidyamandir Classes 8.
For the arrangement shown in figure, the tension in the string to prevent it from sliding down is : (A)
6N
(B)
6.4 N
(C)
0.4 N
(D)
None of these
m =1kg
0 .8
37
9.
An empty plastic box of mass 9 kg is found to accelerate up at rate of g/3 when placed deep inside water. Mass of the sand that should be put inside the box so that it may accelerate down at the rate of g/4 is : (A) 7 kg (B) 6 kg (C) 9 kg (D) None of these
10.
A block of mass M is attached to the lower end of a vertical rope of mass m. An upward force P acts on the upper end of the rope. PM The system is free is move. The force exerted by the rope on the block is M m (A)
in all cases
(B)
Only if the rope is uniform
(C)
in gravity-free space only
(D)
Only if P M m g
VMC/Dynamics of a Particle
71
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [8]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
2.
Blocks A and B have masses of 2 kg and 3 kg respectively. The ground is smooth. P is an external force of 10 N. The force exerted by B on A is : (A) 4N (B) 6N (C) 8N (D) 10 N Two blocks are connected by massless string and pulley. If the blocks are left to move and the wedge is fixed, the force by pulley on the clamp is: (A) (C)
3 3 mg 4
P = 10N N
B
m kg m kg
3 mg 2
(B)
mg
3kg 2kg N A
mg 2
(D)
30
3 4
3.
A block of 10 kg is placed on rough inclined surface find range F of force F along inclined plane so that block remains at rest: m =10 kg (A) 0 < F < 115 (B) 10 < F < 115 (C) 15 < F < 115 30 (D) 10 < F < 100
4.
A car goes on a banked track with angle of banking 37 . It comes across a turn of radius 100 m. If coefficient of friction between the tyres and the surface is (A)
5.
48.38 m/s
1 , then the maximum velocity with which the car can take the turn, assuming g = 10m/s2, is: 3 (B)
55.76 m/s
(C)
27.38 m/s
(D)
None of these
When forces F1 ,F2 ,F3 .......Fn act on a particle, the particle remains in equilibrium. If F1 is now removed then acceleration of the particle
is:
F1 F F2 F3 ... Fn F1 F2 1 (B) (C) (D) m m m m A body of mass 4 kg is moving at speed 2 m/s on circular path of radius 1 m. Speed of particle is continuously increasing at rate of 3 m/s2. Force acting on particle at the instant when speed 2 m/s is: (A) 28 N (B) 12 N (C) 20 N (D) 16 N (A)
6.
7.
A man tried to remain in equilibrium by pushing with his hands and feet against two parallel walls. For equilibrium, (A) he must exert equal forces on the two walls. (B) the forces of friction at the two walls must be equal. (C) friction must be present on both walls. (D) the coefficients of friction must be the same between both walls and the man.
VMC/Dynamics of a Particle
72
HWT/Physics
Vidyamandir Classes 8.
A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth’s surface. A block B placed at the top of the wedge takes a time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will : (A) take a time longer instant, the block will (B) take a time longer than T to slide down the wedge (C) remain at the top of the wedge (D) jump off the wedge
9.
Consider a vehicle going on a horizontal road towards east. Neglect any force by the air. The frictional forces on the vehicle by the road. (A) is towards east if the vehicle is accelerating (B) is zero if the vehicle is moving with a uniform velocity (C) must be towards east (D) must be towards west
10.
In the arrangement shown in figure m1 = 1 kg, m2 = 2 kg. Pulleys are massless and strings are light. For what value of M the mass m1 moves with constant velocity (neglect friction) : (A) 6 kg (B) 4 kg (C) 8 kg (D) 10 kg
M
1
2
m2 m1
VMC/Dynamics of a Particle
73
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [9]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
A cricketer hits a ball of mass 1 kg coming towards him with a velocity of 20 m/s and the ball bounces back with the same speed. If the time of impact is 1/50 second, the total force exerted is : (A) 500 N (B) 1000 N (C) 2000 N (D) 4000 N
2.
A car starts from rest on cover a distance‘s’. The coefficient of kinetic friction between the road and tyres is . The minimum time in which the car can cover the distance‘s’ is proportional to : (A)
3.
(B)
1
(C)
(D)
1
The string between blocks of mass m and 2m is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut find the magnitudes of acceleration of mass 2m and m (immediately after cutting) (A) (C)
g, g g ,g 2
g 2
(B)
g,
(D)
g g , 2 2
4.
Statement 1 : Action and reaction acts on same body. Statement 2 : Newton’s third law states that action and reaction are equal (A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
5.
Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is :
6.
(A)
F 2m
(C)
F x 2m a
a a2 x2
(B)
F 2m
x a2 x2
(D)
F 2m
a2 x2 x
A person standing on the floor of an elevator drops a coin. The coin reaches the floor of the elevator in a time t1 if the elevator is stationary and in time t2 if it is moving uniformly. Then : (A) t1 = t2 (B) t1 < t2 (C) t1 > t2 (D) t1 < t2 or t1 > t2 depending on whether the lift is going up or down
VMC/Dynamics of a Particle
74
HWT/Physics
Vidyamandir Classes 7.
A scooter starting form rest moves with a constant acceleration for a time t1 , then with a constant velocity for the next t2 and finally with a constant deceleration for the next t3 to come to rest. A 500 N man sitting on the scooter behind the driver manages to stay at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is. (A) 500 N throughout the journey (B) less than 500 N throughout the journey (C) more than 500 N throughout the journey (D) > 500 N for time t1 and t3 and 500 N for t2
8.
Consider the situation shown in figure. The wall is smooth but the surface of A and B in contact are rough. The friction on B due to A in equilibrium. (A) is upward F A B (B) is downward (C) is zero (D) the system cannot remain in equilibrium
9.
Suppose all the surfaces in the previous problem are rough. The direction of friction on B due to A. (A) is upward (B) is downward (C) is zero (D) depends on the masses of A and B
10.
A block of mass m slides down on a wedge of mass M as shown in figure. Let a1 be the acceleration of the wedge and a2 the acceleration of block. N1 is the normal reaction
between block and wedge and N2 the normal reaction between wedge and ground. Friction is absent everywhere. Select the correct alternative(s): (A) (B) N2 M m g N1 m g cos | a1| sin (C) (D) N1 sin M | a1| m a2 M a1
VMC/Dynamics of a Particle
75
m M
HWT/Physics
Vidyamandir Classes
DATE :
MARKS : 10
IITJEE :
NAME :
TIME : 25 MINUTES
TEST CODE : DNP [10]
ROLL NO.
START TIME :
END TIME :
STUDENT’S SIGNATURE :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
A cricketer catches a ball traveling at 20 m/s along 60 with the horizontal and stops it within 0.05 s. The average acceleration of the ball is : 200 m/s2
(A)
(B)
200 m / s 2
400 m/s2
(C)
(D)
400 m/s 2
2.
A coin rotates on a table about its centre with w = 10 rad/s. The point on the coin with the maximum speed is : (A) the centre (B) any point at distance r/2 from the centre (C) any point on the rim of the coin (D) all points have equal speed
3.
A small steel ball of mass m is falling in water with speed = 12 m/s. The net downward force at any instant on the ball is : (A) < mg (B) > mg (C) = mg (D) mg
4.
A boy running at speed 3 m/s drops a ball of mass 300 gm. The net force on the ball immediately after the drop is : (g = 10 m/s2). (A) 4.35 N (B) 1.35 N (C) 3N (D) 1.65 N
5.
Force F1 on body m1 and force F2 acts on body m2. (m1 = 5 kg, m2 = 7kg). Their v-t graphs are given. v (m/s)
v (m/s)
20
12
(m1)
(m2)
t (s)
5
3
Then : (A) 6.
F1 4 F2
(B)
F1 9 F2 35
F1 5 F2 7
(C)
t (s) (D)
F1 1 F2
The force-time graph (for a body m = 1 kg) is given_____. F (N) 50
10
20
30
t (s)
50
VMC/Dynamics of a Particle
76
HWT/Physics
Vidyamandir Classes The velocity time graph of the body will be___________. v (m/s)
v (m/s)
50
50
(A)
(B) 10
20
30
t
250
250 (C)
(D)
20 10
10
30
All surfaces are frictionless. The acceleration of A, B and C in order will be : P P2 P P P2 0, 0, 1 0, 2 , 1 (A) (B) 2m m m 0,
P2 P1 , m m
(D)
2 kg
B
A
P2
B
P1
P1 P2 P1 P2 P1 P2 , , m 2m 3m
A
C
3 kg
m m m
A Block of mass 2 kg is moving along a horizontal floor with friction k 1.2 . If its initial velocity is 120 m/s. It will come to rest after time. (A) 1 sec (C) 0.5 sec
10.
t (s)
30
250
A experiences no friction from the table. The tension in the string is : (g = 10 m/s2). (A) 10 N (B) 12 N (C) 50 N (D) Cannot be determined
(C)
9.
20
t (s)
250
8.
30
v (m/s)
v (m/s)
7.
20 t
10
(B) (D)
vi = 120 m/s
1.5 sec 2 sec
k 1 .2
The tension in the string is : (A)
(m1 + m2)g
(C)
m1m2 g m1 m2
VMC/Dynamics of a Particle
(B)
m1
m2 g
m
m22 g
2 1
(D)
m1 m2
77
m1 > m2 m1 m2
HWT/Physics
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