PHYSICS FOR IIT-JEE (MAIN & ADVANCED)

Er. SHRAVAN KATIYAR

AVDANCED SHEET ON FORCE CONCEPT

Subjective Type #
Q.01 A block 'C' of mass m rests on a smooth table . Two blocks A and B each of
mass m, are attached to the end of a light inextensible string passing over a smooth
pulley fixed to C as shown in the figure. B rests on C and A can move in a
frictionless vertical shaft. Find the acceleration of C.

Q.02 In the figure shown C is a fixed wedge. A block B is kept on the inclined surface
of the wedge C. Another block A is inserted in a slot in the block B as shown in figure.
A light inextensible string passes over a light pulley which is fixed to the block B
through a light rod. One end of the string is fixed and other end of the string is fixed to
A.S is a fixed support on the wedge. All the surfaces are smooth. Masses of A and B
are same. Find the magnitude of acceleration of A and B. (sin 37º = 3/5)

Q.03 In the figure shown all blocks are of equal mass ‘m’. All surfaces are smooth. Find the
acceleration of all the blocks.

a
Q.04 A lift L is moving upwards with a constant acceleration a = g. A small block A of mass
' m ' is kept on a wedge B of the same mass ' m '. The height of the vertical face of the wedge A
is ' h'. A is released from the top most point of the wedge. Find the time taken by A to reach L
the bottom of B. All surfaces are smooth and B is also free to move. B h
)q

Q.05 In the arrangement shown in the Fig., the block of mass m = 2 kg lies on the wedge of
mass M = 8 kg. Find the initial acceleration of the wedge if the surfaces are smooth

Q.06 The diagram shows three rings of the same size but different masses. Find out the
minimum and maximum value of the force F that should be applied such that no relative M3
motion starts between the rings.
M1 M2

Q.07 Three identical spheres have been placed on a horizontal surface. A belt has tied the spheres. The belt has zero tension
initially. Now, a fourth identical sphere is place symmetrically on the top of the three spheres. Find out the tension in the
belt.
TOP VIEW
F

Q.08 The diagram shows a uniform chain of N links. Mass of each link is M. A force F = NMg + kt has
been applied as shown. (k is a positive constant and t represents time). The joint between the 4th and 5th link
can tolerate a tension which is thee times the initial value. Find out the time when the breaking will occur.
Draw the variation of tension between the 2nd and the 3rd link as a function of time.

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Q.09 In figure shown, pulleys are ideal m1 > 2 m2. Initially the system is in equilibrium and
string connecting m2 to rigid support below is cut. Find
the initial acceleration of m2?

Q.10 Three identical rigid circular cylinders A, B and C are arranged on smooth
inclined surfaces as shown in figure. Find the least
value of  that prevent the arrangement from collapse.

Q.11 A 20 kg block B is suspended from a cord attached to a 40 kg

cart A . Find the ratio of the acceleration of the block in cases (i)
& (ii) shown in figure immediately after the system is released
from rest.
(neglect friction)

Q.12 In the system shown. Find the initial acceleration of the wedge of mass 5M.
The pulleys are ideal and the cords are inextensible.
(there is no friction anywhere).

Q.13 A smooth right circular cone of semi vertical angle  = tan –1(5/12) is at rest on a horizontal plane. A rubber ring of
mass 2.5kg which requires a force of 15N for an extension of 10cm is placed on the cone. Find the increase in the
radius of the ring in equilibrium.

Q.14 A U shaped container has uniform cross sectional area S. It is suspended vertically with the help
of a spring and two springs A and B as shown in the fig. The spring and strings are light. When water
(density = d) is poured slowly into the container it was observed that the level of water remained
unchanged with respect to the ground. Find the force constant of the spring.

Q.15 A light string passing over a smooth pulley holds two identical buckets at its ends. Mass of
each empty bucket is M and each of them bolds M mass of sand. The system was in equilibrium
when a small leak developed in bucket B (take this time as t = 0). The sand leaves the bucket at a
constant rate of  kg/s. Assume that the leaving sand particles have no relative speed with respect
to the bucket (it means that there is no impulsive force on the bucket like leaving exhaust gases
exert on a rocket). Find the speed (V0) of the two bucket when B is just empty.

 
Q.16 A rope of length   1 R has been placed on a smooth sphere of radius R as
2 
shown in fig. End A of the rope is at the top of the sphere and end B is overhanging.
Mass per unit length of the rope is . The horizontal string holding this rope in place
can tolerate tension equal to weight of the rope. Find the maximum mass (M0) of a
block that can be tied to the end B of the rope so that the string does not break.

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Q.17 In the fig. all pulleys (P1, P2, P3.......) are massless and all the blocks (1, 2, 3........) are identical, each having mass m. The
system consist of infinite number of pulleys and blocks. Strings are light and inextensible and horizontal surfaces are
smooth. Pulley P1 is moved to left with a constant acceleration of a0. Find the acceleration of block 1. Assume the strings
to remain horizontal.

Q.18 Two blocks of equal mass have been placed on two faces of a fixed
wedge as shown in fig. The blocks are released from position where centre
of one block is at a height h above the centre of the other block. Find the
time after which the centre of the two blocks will be at same horizontal
level. There is no friction anywhere.

Q.19 Six identical blocks – numbered 1 to 6-have been glued in two groups of three each and have been
suspended over a pulley as shown in fig. The pulley and string are massless and the system is in
equilibrium. The block 1, 2, 3 and 4 get detached from the system in sequence starting with block 1.
The time gap between separation of two consecutive block (ie., time gap between separation of 1
and 2 or gap between separation of 2 and 3) is t0. Finally, blocks 5 and 6 remain connected to the
string.
a) Find the final speed of blocks 5 and 6.
b) Plot the graph of variation of speed of block 5 with respect to time. Take t = 0 when block
1 gets detached.

Q.20 A uniform chain of mass M = 4.8 kg hangs in vertical plane as shown in

the fig.
a) Show that horizontal component of tension is same throughout
the chain.
b) Find tension in the chain at point P where the chain makes an
angle  = 15o with horizontal.
c) Find mass of segment AP of the chain.
(Take g = 10 m/s2; cos 15o = 0.96, sin 15o = 0.25).

Q.21 Three identical smooth balls are placed between two vertical walls as shown in fig. Mass of
5R
each ball is m and radius is r  where 2R is separation between the walls.
9
a) Force between which two contact surface is maximum? Find its value.
b) Force between which two contact surface is minimum and what is its value?

Q.22 A smooth rod is fixed at an angle a to the horizontal. A small ring of mass m can slide along the rod. A thread carrying a
small sphere of mass M is attached to the ring. To keep the system in equilibrium, another thread is attached to the ring
which carries a load of mass m0 at its end (see fig.). The thread runs parallel to the rod between the ring and the pulley. All
threads and pulley are massless.

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 a) Find m0 so that system is in equilibrium.
b) Find acceleration of the sphere M immediately after the thread supporting m0 is cut.
Q.23 Two hemispheres of radii R and r (< R) are fixed on a horizontal table touching each other (see fig.). A uniform rod rests
on two spheres as shown. The coefficient of friction between the rod and two spheres is . Find the minimum value of the
r
ratio for which the rod will not slide.
R

Q.24 A rope of mass m is hung from a ceiling. The F. The tangent to the rope at its ends makes an angle  with horizontal ceiling.
The two tangents at the lower point make an angle of  with each other. Find .

Q.25 A smooth cylinder is fixed with its axis horizontal. Radius of the cylinder is R. A uniform
rope (ACB) of linear mass density  (kg/m) is exactly of length R and is held in semicircular
shape in vertical plane around the cylinder as shown in fig. Two massless strings are connected
at the two ends of the rope and are the pulled up vertical with force T0 to keep the rope in
contact with the cylinder.
a) Find minimum value of T0 so that the rope does not lose contact with the cylinder
at any point.
b) If T0 is decreased slightly below the minimum value calculated in (a), where will
the rope lose contact with the cylinder.

Q.26 A hemisphere of mass M and radius R rests on a smooth horizontal table. A vertical rod of mass m is held between two
smooth guide walls supported on the sphere as shown. There is no friction between the rod and the sphere. There is no
friction between the rod and the sphere. A horizontal string tied to the sphere keeps the system at rest.

a) Find tension in the string.

b) Find the acceleration of the hemisphere immeidately after the string is cut.

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