Page 1 of 2 CPP - SANKALP_WEP–9-PH-II

CPP
WORK ENERGY POWER - SHEET: 9(Lecture–9&10)

LEVEL – I
1. A block of mass 1 kg is placed at the point A of a rough track shown in the A
B
figure. If slightly pushed towards right, it stops at the point B of the track.
Calculate the work done by the frictional force on the block during its transit 1.0 m 0.8 m
from A to B.

2. The two block in an Atwood machine have masses 2.0 kg and 3.0 kg. Find the work done by gravity during
the fourth second after the system is released from rest.

3. Consider the situation shown in the figure. The system is released from rest and the block 4.0 kg
of mass 1.0 kg is found to have a speed o.3 m/s after it has descended through a distance
of 1 m. Find the coefficient of kinetic friction between the block and the table.
1.0 kg

4. A car weighing 1400 kg is moving at a speed of 54 km/h up a hill when the motor stops. If it is just able to
reach the destination which is at a height of 10 m above the point, calculate the work done against friction
(negative of the work done by the friction).

5. In the figure shows a particle sliding on a frictionless track which terminates

in s straight horizontal section. If the particle starts slipping from the point A,
1.0 m 0.5 m
how far away from the track will the particle hit the ground?

6. A block weighing 10 N travels down a smooth curved track AB joined to a rough A

horizontal surface in the figure. The rough surface has a friction coefficient of 0.20
with the block. If the block starts slipping on the track from a point 1.0 m above 1.0 m
the horizontal surface, how far will it move on the rough surface?
B

7. A uniform chain of length L and mass M overhangs a horizontal table with its two third part on the table. The
friction coefficient between the table and the chain is . Find the work done by the friction during the period
the chain slip off the table.

LEVEL – II

1. 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 ideal spring of
force constant 6 N/m after travelling a distance of 0.25 m. Assume
acceleration due to gravity is 10 m/s2. Find the final displacement of
the particle from its starting point.

2. 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 = 20cm. After the particle is released, it slides down the ring
the contact force between the particle & the ring becomes zero when it reaches
the lowest position B. Determine the force constant of the spring.

3. A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at

t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of
the same mass as P is ejected from A at t=0 along the horizontal string AB, with the
speed v. Friction between the bead and the string may be neglected.
Which bead reaches point B earlier?
FIITJEE Ltd., ICES House, Sarvapriya Vihar (Near Hauz Khas Bus Terminal), New Delhi - 16, Ph : 6515949 , 6865182, 6854102, Fax : 6513942
Page 2 of 2 CPP - SANKALP_WEP–9-PH-II

O
4. The bob of a pendulum is released from a horizontal position A as shown in A
figure. If the length of the pendulum is 2 m, what is the speed with which the bob 900

arrives at the lowermost point B, given that it dissipated 10% of its initial energy
against air resistance?

5. A block of mass 100 g is moved with a speed of 5.0 m/s at the highest point in a closed circular tube of radius
10 cm kept in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block
makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube
2
on block during the process. (Take g = 10 m/s .)

6. A uniform chain of mass m and length  overhangs a table with its two third part on the table. Find the work to
be done by a person to put the hanging part back on the table.

7. A chain of length and mass m lies on the surface of a smooth hemisphere of

radius R  I with one end tied to the top of the hemisphere. Find the gravitational
potential energy of the chain with reference level of the top of the hemisphere?

8. A string with one end fixed on a rigid wall passing over a fixed frictionless pulley 2m
at a distance of 2m from the wall, has a point mass M = 2kg attached to it at a M
distance of 1 m, from the wall. A mass m = 0.5 kg attached at the free end is 1m
held at rest so that the string is horizontal between the wall and the pulley, and
vertical beyond the pulley. What will be the speed with which the mass M will hit
the wall when mass m released? m

——
ANSWERS
WORK ENERGY POWER – SHEET – 9(Lecture–9&10)
LEVEL - I
1. 2 J
2. 67 J
3. 0.12
4. 17500 J
5. At a horizontal distance of 1 m from the end of the track.
6. 5.0 m
7. 2 MgL/9

LEVEL - II
1. 1.25 m
2. 500N/m
3. P
4. 6 m s–1.
5. 1.45 J
6. mgl/18
mR2g  
7. sin R  R 
 
8. v = 3.35 m/s.

FIITJEE Ltd., ICES House, Sarvapriya Vihar (Near Hauz Khas Bus Terminal), New Delhi - 16, Ph : 6515949 , 6865182, 6854102, Fax : 6513942