# Jee-2014-Booklet3-Hwt-system of Particles & Rotational Motion

August 28, 2017 | Author: varunkohliin | Category: Rotation Around A Fixed Axis, Angular Momentum, Orbit, Mass, Mechanical Engineering

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Jee-2014-Booklet3-Hwt-system of Particles & Rotational Motion...

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Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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 T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at a point P Parallel to AB, such that the object has only the translational motion without rotation. Find the distance of P from to C. (A) (C)

2 l 2 4 l 3

(B)

3 l 2

(D)

l

2.

A circular disc of radius R is removed form a bigger circular disc of radius 2R, such that the circumference of the discs coincide. The distance of centre of mass of the new disc is Rα from the centre of the bigger disc. The value of  is : (A) 1/3 (B) 1/2 (C) 1/6 (D) 1/4

3.

When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many rotations will it make before coming to rest ? Assume constant resistive torque (A) 24 (B) 36 (C) 18 (D) 12

4.

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is : (A)

5.

3 5

(B)

12  3

(C)

1 3

(D)

5 6

Four balls each of radius 10 cm and mass 1 kg, 2kg, 3kg and 4 kg are attached to the periphery of massless plate of radius 1m. What is moment of inertia of the system about the centre of plate ? (A)

12.04 kg  m 2

(B)

10.04 kg  m 2

(C)

11.50 kg  m 2

(D)

5.04 kg  m 2

6.

A solid sphere is rotating in free space. If the radius of sphere is increased keeping mass same which one of the following will not be affected ? (A) Angular velocity (B) Angular momentum(C) Moment of inertia (D) Rotational kinetic energy

7.

A force of 200 N acts tangentially on the rim of a wheel 25cm in radius. Find the torque. (A) 50 Nm (B) 150 Nm (C) 75 Nm (D)

8.

39 Nm

A disc of moment of inertia 5kg  m 2 is acted upon by a constant torque of 40 Nm. Starting from rest the time taken by it to acquire an angular velocity of 24 rads –1 is : (A) 3s (B) 4s

VMC/System of Particles & Rotational Motion

(C)

47

2.5 s

(D)

120 s

HWT/Physics

Vidyamandir Classes 9.

A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 10ms 1 . It then rolls up a smooth inclined plane of inclination

30 with the horizontal. The height attained by sphere before it stops is: (A) 700 cm (B) 701 cm (C) 7.1 m 10.

(D)

None of these

The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle  is: (A) (B) (C) (D) g sin  2 / 3 g sin 1 / 2 g sin  1 / 3 g sin

VMC/System of Particles & Rotational Motion

48

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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.

The centre of mass of three particles of masses 1 kg, 2kg and 3 kg is at (3, 3, 3) with reference to a fixed coordinate system. Where a fourth particle of mass 4 kg should be placed, so that the centre of mass of the system of all particles shifts to a point (1, 1, 1) ? (A) (B) (C) (2, 2, 2) (D) (1, 1, 1) ( 1  1  1) ( 2  2  2) Two bodies of 6kg and 4kg masses have their velocity 5i  2 j  10k and 10i  2 j  5k respectively. Then the velocity of their centre of mass is: (A) 5i  2 j  8k

(B)

7i  2 j  8k

(C)

7i  2 j  8k

(D)

5i  2 j  8k

3.

The angular velocity of a wheel increases from 100 rps to 300 rps in 10 s. The number of revolutions made during that time is: (A) 600 (B) 1500 (C) 1000 (D) 2000

4.

Moment of inertia of big drop is I. If 8 droplets are formed from big drop, then moment of inertia of small droplet is: I I I I (A) (B) (C) (D) 32 16 8 4

5.

Four point masses, each of value m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD is: (A)

6.

(B)

3ml 2

(C)

3ml 2

(D)

ml 2

A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity ω . Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be : (A)

7.

2ml 2

(B)

M ω 4m

A couple produces : (A) no motion (C) purely rotational motion

(C)

 M  4m   ω  M 

(B) (D)

linear and rotational motion purely linear motion

(D)

  M  M  4m  ω

8.

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which of the following will not be affected ? (A) Moment of inertia (B) Angular momentum (C) Angular velocity (D) Rotational kinetic energy

9.

A solid sphere is rolling without slipping on a horizontal surface. The ratio of its rotational kinetic energy to its translational kinetic energy is : (A) 2/9 (B) 2/7 (C) 2/5 (D) 7/2

10.

A solid cylinder is rolling down on an inclined plane of angle  . The coefficient of static fraction between the plane and cylinder is  s . Then condition for the cylinder not to slip is : (A)

tan   3 s

(B)

tan   3 s

VMC/System of Particles & Rotational Motion

(C)

49

tan   3 s

(D)

tan  3 s

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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 pulley fixed to the ceiling carries a string with blocks of masses m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be: g 4 g g  (C) (D) 2 2 Consider a two particle system with particles having masses m1 and m2. If the first particles is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

(A)

2.

3.

m2 d m1

(B)

(C)

m1 d m2

(D)

(B) (D)

m1 d m1  m2

(C)

 1 M R 2

 r 

4

4

(B)

mL2 12

(C) (D)

If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take: (A) 96h (B) 48 h (C) 6h (D) 1.5 h

7.

What is moment of inertia in terms of angular momentum (L) and kinetic energy (K)? (A)

(B) (D)

1 M  R4  r 4 2

(B)

L2 2K

(C)

L 2K

2

(D)

L 2k

A particle of mass 1 kg is projected with an initial velocity 10ms–1 at an angle of projection 45° with the horizontal. The average torque acting on the projectile, between the time at which it is projected and the time at which it strikes the ground, about the point of projection in Newton-meter is: (A) 25 (B) 50 (C) 75 (D) 100

9.

The moment of inertia of a flywheel having kinetic energy 360 J and angular speed of 20 rads–1 is : (A) 18 kg m2 (B) 1.8 kg m2 (C) 2.5 kg m2 (D) 9 kg m2

10.

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle  . The frictional force.: (A) converts translational energy to rotational energy (B) dissipates energy as heat (C) decreases the rotational motion (D) decreases the rotational and translational motion

A T joint is formed by two identical rods A and B each of mass m and length L in the XY plane as shown. Its moment of inertia about axis coinciding with A is:

VMC/System of Particles & Rotational Motion

L2 K

8.

1 M R2  r 2 2

mL2 6 None of these

6.

d

From a disc of radius R, a concentric circular portion of radius r is cut out so as to leave an annular disc of mass M. The moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its centre of gravity is: 1 M R2  r 2 2

2mL2 3

The instantaneous velocity of a point B of the given rod of length 0.5m is 3ms–1 in the represented direction. The angular velocity of the rod for minimum velocity of end A is:

(A)

5.

(B)

(A)

(A) (C) 4.

zero

(A)

50

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

  MARKS :    10 

TIME : 25 MINUTES

TEST CODE : RTM 

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.

2.

3.

4.

5.

6.

A system consists of 3 particles each of mass m located at points (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are: (A) (6, 6) (B) (3, 3) (C) (1, 1) (D) (2, 2) A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc, (A) 0.4 cm (B) 2.4 cm (C) 1.8 cm (D) 1.2 cm Identify the increasing order of the angular velocities of the following : 1. Earth rotating about its own axis 2. Hour’s hand of a clock 3. Second’s hand of a clock 4. Flywheel of radius 2m making 300 rpm (A) 1, 2, 3, 4 (B) 2, 3, 4, 1 (C) 3, 4, 1, 2 (D) 4, 1, 2, 3

7.

8.

9.

Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corner is: (A) 5/67 ma2 (B) 1/12 ma2 2 (C) 7/12 ma (D) 2/3 ma2 The angular momentum of a particle describing uniform circular motion is L. If its kinetic energy is halved and angular velocity doubled, its new angular momentum is: (A) 4L (B) L/4 (C) L/2 (D) 2L (E) L/8

(C)

zero mv 2h 2

(B)

mvh 2 2

(D)

mvh 2

VMC/System of Particles & Rotational Motion

(A)

(B)

(C)

(D)

Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = Mv is imparted to the body at one of its ends, what would be its angular velocity?

(A)

v/ L

(B)

2 v/ L

(C)

v / 3L

(D)

v / 4L

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of

3v 2 with respect to the initial 4g

position. The object is:

(A) (C) 10.

A particle is projected with a speed v at 45° with the horizontal. The magnitude of angular momentum of the projectile about point of projection when the particle is at its maximum height h is: (A)

A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30 rads–1. What is angular velocity, if a mass of 0.25 kg is put on periphery of the disc?

48

ring hollow sphere

(B) (D)

solid sphere disc

A ring starts to roll down the inclined plane of height h without slipping. The velocity with which it reaches the ground is: (A)

10 gh 7

(B)

4 gh 7

(C)

4 gh 3

(D)

gh

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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 particles A and B initially at rest, move towards each other, under mutual force of attraction. At an instance when the speed of A is v and speed of B is 2v, the speed of centre of mass (CM) is : (A) zero (B) v (C) 2.5v (D) 4v

2.

If the external forces acting on a system have zero resultant, the centre of mass : (A) may move but not accelerated (B) may accelerate (C) must not move (D) None of the above

3.

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at a point near the rim of the disc, moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc. (A) continuously decreases (B) continuously increases (C) first increases and then decreases (D) remains unchanged

4.

The moment of inertia of a rod about an axis through its centre and perpendicular to its is

1 ML2 (where M is the mass and L is 12 the rod). The rod is bent in the middle so that the two halves make an angular of 60°. The monument of inertia about same axis would be:

(A)

1 ML2 48

(B)

1 ML2 12

(C)

1 ML2 24

(D)

ML2 8 3

5.

A wheel of moment of inertia 2.5kg – m2 has an initial angular velocity of 40 rads–1. A constant torque of 10 Nm acts on the wheel. The time during which the wheel is accelerated to 60 rads–1 is: (A) 4s (B) 6s (C) 5s (D) 2.5 s

6.

When the distance between earth and sun is halved, the duration of year will become. (A) more (B) less (C) can’t be determined (D)

7.

None of the above

A stone of mass m tied to a string of length l is rotating along a circular path with constant speed v. The torque on the stone is : (A)

mlv

(B)

mv l

(C)

mv 2 l

(D)

zero

8.

A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at bottom of the inclined plane is v. The kinetic energy of the sphere at the bottom is : 7 2 2 5 2 1 2 mv 2 mv mv mv (A) (B) (C) (D) 10 5 3 2

9.

A body rolls down an inclined plane. If its kinetic energy of rotation is 40% of its kinetic energy of translation, then the body is: (A) solid cylinder (B) solid sphere (C) disc (D) ring

10.

A circular disc of radius R rolls without slipping along the horizontal surface with constant velocity v0 . We consider a point A on the surface of the disc. Then the acceleration of the point A is : (A) constant in magnitude as well as direction (B) (C) constant in magnitude (D)

VMC/System of Particles & Rotational Motion

49

constant in direction constant

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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.

Two point objects of mass 1.5g and 2.5g respectively are at a distance of 16cm apart, the centre of gravity is at a distance x from the object of mass 1.5g, where x is : (A) 10 cm (B) 6 cm (C) 13 cm (D) 3 cm

2.

A body A of mass M while falling vertically downwards under gravity breaks into two parts ; a body B of mass 1/3M and a body C of mass 2/3M. The centre of mass of bodies B and C taken together shift compared to that of body A towards (A) depends on height of breaking (B) does not shift (C) body C (D) body B

3.

A pulley of radius 2 m is rotating about its axis by a force F = (20t – 5t2) N (where t is measured in second) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10kgm 2 , the number of rotations made by the pulley before its direction of motion is reserved, is: (A) more than 3 but less than 6 (C) more than 9

(B) (D)

more then 6 but less than 9 less than 3

4.

A thin wire of mass M and length L is bent to form a circular ring. The moment of inertia of this ring about its axis is: 1 1 1 1 ML2 (A) (B) (C) (D) ML2 ML2 ML2 2 2 2 12 4 3 

5.

A boy and a man carry a uniform rod of length L, horizontally in such a way that boy gets 1/4th load. If the boy is at one end of the rod, the distance of the man from the other end is: (A)

6.

L 3

(B)

L 4

(C)

2L 3

(D)

3L 4

A uniform rod AB of length l and mass m is free to rotate about point A. a horizontal axis perpendicular to the rod passing through the end. The rod is rest in the horizontal position. The initial angular acceleration of the rod will be: (A)

2g 3l

(B)

mg

(C)

3 gl 2

(D)

3g 2l

l 2

7.

A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 1 kg – m2 and its rate of rotation 2 rvs/s. The angular momentum is: (A) 1.257 kg m2s–1 (B) 12.57 kg m2s–1 (C) 13.57 kg m2s–1 (D) 20 kg m2s–1

8.

A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω . Its centre of mass rises to a maximum of (A)

1 l 2 2 3 g

(B)

1 l 6 g

VMC/System of Particles & Rotational Motion

(C)

50

1 l 2 2 2 g

(D)

1 l 2 2 6 g

HWT/Physics

Vidyamandir Classes 9.

A thin metal disc of radius of 0.25m and mass 2kg starts from rest and rolls down on an inclined plane. If its rotational kinetic energy is 4 J at the foot of inclined plane, the linear velocity at the same point, is in ms 1 . (A)

10.

2

(B)

(C)

2 2

2 3

(D)

3 2

An annular ring with inner and outer radii R1 and R2 is rotating with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1 / F2 is: (A)

R2 R1

(B)

 R1     R2 

2

VMC/System of Particles & Rotational Motion

(C)

51

1

(D)

R1 R2

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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.

Identify the correct statements for the rotational motion of a rigid body. (A) Individual particles of the body do not undergo accelerated motion (B) The centre of mass of the body remains unchanged (C) The centre of mass of the body moves uniformly in a circular path (D) Individual particles and centre of mass the body undergo an accelerated motion

2.

The distance of the center of mass of the T-shaped plate from O is :

3.

(A)

7m

(B)

1.7 m

(C)

4m

(D)

1m

The moment of inertia of a thin uniform rod of length L and mass M about an axis passing through a point at a distance of 1/3 from one of its ends and perpendicular to the rod is: (A)

4.

(C)

7 ML2 48

(D)

ML2 48

x 3

(B)

x 2

(C)

3 x 2

(D)

x 2

2M g M  2m

(B)

2m g M  2M

(C)

M  2m g 2M

(D)

2M  m g 2M

A force of  F k acts on O, the origin of the coordinate system. The torque about the point (1, –1) is: (A) (B) F (i  j )  F (i  j )

(C) 7.

ML2 9

A uniform disc of mass M and radius R is mounted on a fixed horizontal axis. A block of mass m hangs from a massless string that is wrapped around the rim of the disc. The magnitude of the acceleration of the falling block (m) is: (A)

6.

(B)

Three identical rods, each of length x, are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the triangle is: (A)

5.

ML2 12

F (i  j )

(D)

 F (i  j )

A particle of mass m = 5 units is moving with a uniform speed v  3 2 m in the XOY plane along the line Y = X + 4. The magnitude of the angular momentum about origin is: (A) zero (B) 60 unit (D)

40 2 unit

(E)

(C)

7.5 unit

3.0 unit

VMC/System of Particles & Rotational Motion

52

HWT/Physics

Vidyamandir Classes 8.

A body is rotating with angular velocity 30rads–1. If its kinetic energy is 360 J, then its moment of inertia is: (A) 0.8 kgm2 (B) 0.4 kgm2 (C) 1 kgm2 (D) 1.2 kgm2

9.

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley a perfect uniform circular disc, of same mass , the acceleration of the mass m, if the string does not slip on the pulley, is: 2 g 3 g g (A) g (B) (C) (D) 3 3 2

10.

A cylinder rolls down an inclined plane of inclination 30°, the acceleration of cylinder is: (A) g/3 (B) g (C) g/3 (D)

VMC/System of Particles & Rotational Motion

53

2g/3

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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.

Statement : I

If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.

Statement : II

The linear momentum of an isolated system remains constant.

(A) (B) (C) (D) 2.

Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I Statement-I is True, Statement-II is True and Statement-II is NOT a correct explanation for Statement-I Statement-I is True, Statement-II is False Statement-I is False, Statement-II is True

Two particles of equal mass have velocities v1  4i and v2  4 j ms 1 . First particle has an acceleration a1  (5i  5 j ) ms 2 , while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of (A) straight line (B) parabola (C) circle (D) ellipse

3.

Moment of inertia of a disc about a diameter is I. Find the moment of inertia of disc about an axis perpendicular to its plane and passing through its rim? (A) 6I (B) 4I (C) 2I (D) 8I

4.

For the given uniform square lamina ABCD, whose centre is O. (A)

2 I AC  I EF

(B)

I AD  4 I EF

(C)

I AC  I EF

(D)

I AC  2 I EF

5.

A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4m distance from the hinges for opening or closing the door is: (A) 1.2 N (B) 3.6 N (C) 2.4 N (D) 4N

6.

A round disc of moment of inertia I2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I1 rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is: I 2ω I1ω ( I1  I 2 )ω (A) (B) (C) (D) ω I1  I 2 I1  I 2 I1

7.

A particle performs uniform circular motion with an angular momentum L. If the frequency of particle’s motion is doubled and its KE is halved, the angular momentum becomes. (A) L/2 (B) 2L (C) 4L (D) L/4

VMC/System of Particles & Rotational Motion

54

HWT/Physics

Vidyamandir Classes 8.

The moments of inertia of two freely rotating bodies A and B are IA > IB and their angular momenta are equal. If KA and KB are their kinetic energies, then: (A) KA = KB (B) KA  KA (C) KA < KB (D) KA = 2KB

9.

A solid sphere of mass 1 kg, radius 10 cm rolls down an inclined plane of height 7 m. The velocity of its centre as it reaches the ground level is: (A) 7 m/s (B) 10 m/s (C) 15 m/s (D) 20 m/s

10.

A disc is rolling (without slipping) on a horizontal surface C is its centre and Q and P are two points equidistant from C. Let vP, vQ and vC be the magnitude of velocities of points P, Q and C respectively, then : (A) vQ < vC > vP (B) vQ < vC < vP (C)

vQ  vP  vC 

1 vp 2

VMC/System of Particles & Rotational Motion

(D)

55

vQ  vC  vP

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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.

2.

3.

4.

5.

Two particles of equal mass m go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is:

(B)

2GM 4 2 5 7R

(A)

Gm R

(B)

Gm 4R

(C)

GM 4R

(C)

GM 3R

(D)

Gm 2R

(D)

2GM 5R

Two balls, each of radius R, equal mass and density are placed in contact, then the force of gravitation between them is proportional to: 1 (A) (B) F FR R2 1 F (C) (D) F  R4 R Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth in size is g and that on the surface of the new planet is g  ,

7.

2 1

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is

11kms 1 , the escape velocity from the surface of the planet would be:

8.

(A)

1.1kms 1

(B)

11kms 1

(C)

110 kms 1

(D)

0.11kms 1

The escape velocity of a projectile on the earth’s surface

then: (A)

g  2g

(B)

g   3g

is 11.2 kms 1 . A body is projected out with thrice this speed. The speed of the body far away from the earth will be:

(C)

g  4g

(D)

g  5g

(A)

22.4 kms 1

(B)

31.7 kms 1

(C)

33.6 kms 1

(D)

None of these

If the earth stops rotating, the value of g at the equator (A) increases (B) decreases (C) no effect (D) None of these The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct? h 3h d d (A) (B) 2 2 (C)

6.

2GM 4 2 5 7R

(A)

d  2h

(D)

9.

10.

d h

A thin uniform annular disc (see figure) of mass M has outer radius 4R & inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is:

VMC/System of Particles & Rotational Motion

A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth; R being the radius of the earth. What will be the time period of another satellite at a height 2.5R from the surface of the earth? (A)

6 2h

(B)

6 gR

(C)

6 3h

(D)

12h

A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is: (A)

56

2E

(B)

E

(C)

E/2

(D)

E

HWT/Physics

Vidyamandir Classes

DATE :

  MARKS :    10 

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : RTM 

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.

Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is:

(A) 2.

4.

5.

6.

(B)

3GM 2L

(C)

3GM L

(D)

2GM 3L

(E)

GM 3L

A body is taken to a height of nR from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is:

(A) 3.

GM L

(n + 1)2

(B)

(n + 1)–2

(C)

(n + 1)–1

(D)

(n + 1)

The height at which the acceleration due to gravity becomes g / 9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is: R R (A) 2R (B) (C) (D) 2R 2 3 g The acceleration due to gravity becomes   (g = acceleration due to gravity on the surface of the earth) at a height equal to: 2 (A) 4R (B) R/4 (C) (D) R/2 2R

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is: 4Gm 6Gm 9Gm   (A) (B) (C) (D) zero r r r The escape velocity from the earth is 11 kms–1. The escape velocity from a planet having twice the radius and same mean density as that of earth is: (A)

5.5 kms 1

(B)

11 kms 1

(C)

22 kms 1

(D)

None of these

7.

Energy required to move of a body of mass m from an orbit of radius 2 R to 3R if it is orbiting around a planet of mass M is: (A) GMm/12R2 (B) GMm/3R2 (C) GMm/8R (D) GMm/6R

8.

A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is: (A) 4:1 (B) 1:8 (C) 8:1 (D) 1:4 (E) 1:2

9.

A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at (A) D (B) B (C) A (D) C

10.

Two satellites A and B go round a planet in circular orbits having radii 4R and R, respectively. If the speed of satellite A is 3v, then speed of satellite B is: (A)

3v 2

(B)

4v 2

VMC/System of Particles & Rotational Motion

(C)

57

6v

(D)

12v

HWT/Physics