DPP_WPE

WORK, ENERGY ENERGY AND POWER

1 DPP DP P – 15

1.

Two bodies are projected vertically upwards from one point with the same initial velocity of v0 m/s. The second body is thrown  s after the first. The two bodies meet after time v v v v   (a) 0  (b) 0   (c) 0  (d) 0   2g g 2 g g 2

2.

All the surfaces shown in figure are smooth. If T  A and T  B are the tension in strings connected to block  A and  B respectively, then T  A / T  B is (Pulley and strings are ideal)

3.

(a) 3 : 1

(b) 1 : 1

(c) 2 : 3

(d) 3 : 2

3kg

1kg

 A

B

C 

10kg

A log of mass m is pulled at a constant velocity and with a force F  by means of a rope of length l. The distance between the end of the rope and the ground is h as shown. The co-efficient of friction between the log and the ground is

 h2 (a) mgl  Fh  F 

l

h

F  l 2

Fh mgl

O

 h2 (b) mgl  Fh

F  l 2

(c)

F  l

2

Fh

(d)

 h2

mgl

 F 

l

2

 h2

4.

The work done by a force F   (6 x 3iˆ) N in displacing displacing a particle particle from x = 4 m to x = –2 m is (a) –240 J (b) 360 J (c) 420 J (d) will depend upon the path

5.

Figure shows three situations involving a plane that is not frictionless and a block sliding along the plane. The block begins with the same speed in all three situations and slides until the frictional force has stopped it. Rank the situations according to the increase in thermal energy due to the sliding (neglecting losses to surrounding), in order taking the greatest first.

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(a) (ii), (i), (iii) 6.

(b) (iii), (i), (ii)

(c) (ii), (iii), (i)

(d) (iii), (ii), (i)

Two bars of masses m1 and m2, connected by light undeformed horizontal spring are lying on a rough horizontal surface, having coefficient of friction . Find the minimum constant force (in N) that has to be applied applied horizontally horizontally to the bar m1 along the length of the spring, in order just to shift the bar m2. (Tak (Takee m1 = 10 kg, m2 = 4 kg,  = 0.2 and g = 10 m/s m/s2)

WORK, ENERGY AND POWER

2

A force F   8( x iˆ   y ˆj ) acts on a particle moving in the  x-y  plane. Starting from origin, the 

7.

 particle is taken to (2, 2) and then to on the particle.

8.





2 , 0 . Find the total work done (in J) by the force F 

A particle of mass 5 kg is free to slide on a smooth ring of radius r  = 20 cm fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed to the top point O of the ring. Initially the particle is at rest at a point  A of the ring such that   OCA = 60°, C  being the centre of the ring. The natural length of the spring is also equal to r = 20 cm. After the particle is released and slides down the ring the contact force between the particle and the ring becomes zero when it reaches the lowest position  B. Determine the force constant (in N/m) of the spring.

WORK, ENERGY AND POWER

3 DPP – 16

1.

A projectile is thrown horizontally from top of a building of height 10 m with certain speed u. At the same time another projectile is thrown from ground 10 m away from the building with equal speed u on the same vertical plane. If they collide after 2 s, then (a) the angle of projection for second projectile is 60º and u  10 ms 1  (b) the angle of projection for second projectile is 90º and u  5 ms 1

(c) the angle of projection for second projectile is 60º and u  5 ms 1 (d) the angle of projection for second projectile is 45º and u  10 ms 1 2.

3.

A block of mass m is released from rest when the extension in the spring is  x0. The maximum downward displacement of the block is  Mg  Mg (a) (b)  x 0  x0 2k  2k  2 Mg 2 Mg (c) (d)  x0  x 0 k  k 

k 

M 

A block of mass 2 kg is hanging over a smooth and light  pulley through a light string. The other end of string is  pulled by a constant force F . The kinetic energy of block increases by 16 J in 2s, then

F 

2kg

(a) Force F may be 24 N. (b) Force F must be 24 N. (c) Potential energy must increase. (d) Potential energy must decrease. 4.

5.

At a given instant,  A is moving with velocity of 4 m/s upwards. The velocity of B at that time is (a) 4 m/s (b) 8 m/s (c) 12 m/s (d) 16 m/s In the diagram shown, there is no friction at any contact surface. Initially, the spring has no deformation. Consider all the strings to be sufficiency large and the spring constant to be K . The maximum deformation in the spring will be (a) 4F / 3K  (b) 8F / 3K  (c) F / 3K 

 A

B

(d) none of these

WORK, ENERGY AND POWER

4

6.

A flexible chain of mass   per unit length and length equal to 1/4 of the circumference of the fixed cylinder of radius r  is released from the rest in the horizontal dotted position, with end  B is secured to the top of the cylinder. When the chain finally comes to rest with end  A at C , determine the loss of 4 energy (in J) of the system. (Take  = unit, r  = 2m and 2 g  10 m/s 2 )

7.

Water is pumped from a depth of 10 m and delivered through a pipe of cross section 10  –2 m2 upto a height of 10 m. If it is needed to deliver a volume 0.2 m 3  per second, find the power (in kW) required. [T ake g = 10 m/s 2 ]

8.

A spring is attached with a block of mass m and a fixed horizontal rod. The block is lying on a smooth horizontal table and initially the spring is vertical and unstretched. Natural length of spring is 3 l0. A constant horizontal force F  is applied on the block so that block moves in the direction of force. When length of the spring becomes 5 l0  block leaves contact with the table. Find the constant force F  (in N), if initial and final velocity of block is zero. (Take m = 12 kg and g = 10 m/s2)

WORK, ENERGY AND POWER

5 DPP – 17

1.

A chain of mass per unit length  = 2 kg/m is pulled up by a constant force F . Initially the chain is lying on rough surface and passes onto the smooth surface. The coefficient of friction between chain and rough surface is  = 0.1. The length of the chain is  L. The velocity of the chain when x = L is (a)

2.

F    L

F   2 L

(c)

F   4 L

F 

Rough

(d)

 

Smooth

F  

 L

2

If the range of a gun which fires a shell with muzzle speed V  is  R, then the angle of elevation of the gun is

 V 2    (a) cos   Rg     1

3.

(b)

 x

  gR  (b) cos  2   V    1

(c)

1  V 2  

  2   Rg 

(d)

1 2

 gR    V 2  

sin 1 

A block ‘ A’ of mass 45 kg is placed on a block ‘ B’ of mass 123 kg. Now block ‘ B’ is displaced by external agent by 50 cm horizontally towards right. During the same time block ‘ A’ just reaches to the left end of block  B. Initial & final position are shown in figure. The work done by frictional force on block  A in ground frame during above time is (a) –18 Nm

(b) 18 Nm

(c) 36 Nm

(d) –36 Nm

4.

A straight smooth track ends up in a circular arc of length l and radius  R. A small body is given a velocity v on the straight part of the track. The maximum height above the  R horizontal part attained by body is h. If v = 2 gR and l  , value of h will be 2 3 R 3 R (a) R (b) (c) (d) 2 R 2 4

5.

A person trying to loose weight, lifts a 10 kg mass up to a height of 0.5 m, 1000 times daily. Fat supplies 4  10 7 J of energy per kilogram which is converted into potential energy to raise the weight with 20% efficiency. The potential energy lost, each time the person lowers the mass is dissipated. In 10 days, the amount of fat that the person will use is (a) 6.25  10 2 kg (b) 12.5  10 2 kg (c) 25  10 2 kg (d) 3.125  10 2 kg

6.

A particle of mass 1 kg is given a horizontal velocity of 4 m/s along a horizontal surface, with which it has a coefficient of friction (both static and kinetic) of 0.4. The particle strikes a fixed

WORK, ENERGY AND POWER

6

ideal spring of force constant 6 N/m after travelling a distance of 0.25 m. Assume acceleration due to gravity is 10 m/s 2. Find the final displacement (in cm) of the particle from its starting point.

7.

Force F  is given by F   (6 x 2 y  8 y 2 ) iˆ  ( 2 x 3  16 xy ) jˆ . Find the work done (in J) by this force in moving a particle of mass 1 kg from (2, 4) to (1, 2).

8.

A weightless rod of length l with a small load of mass m at the end is hinged at point  A as shown in the figure and occupies a strictly vertical position, touching a body of mass  M . A light jerk sets the system in motion. For what mass ratio  M /m will the rod form an angle  = /6 with the horizontal at the moment of the separation from the body?

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