1
Varun JEE Advanced (2025)
Laws of Motion
Single Correct Type:
1.
String is massless and pulley is smooth in the
adjoining figure. Total mass on left hand side of the
pulley is m1 and on right hand side is m2. Friction
1
coefficient between block B and the wedge is  =
2
and  = 30°. Select the wrong option.
3.
Time limit 90 minutes
Three blocks of equal mass M are initially at rest on
smooth floor. A force F is applied to the system so
that the three blocks are to move together. Mark the
correct option.
(1) The minimum coefficient of friction required is
F
3Mg
(2) The minimum coefficient of friction required is
F
Mg
(3) The minimum coefficient of friction required is
(1) block B will slide down if m1 = m2
(2) block B may remain stationary with respect to
wedge for suitable values of m1 and m2 with
m2 > m1
(3) block B can not remains stationary with respect
to wedge in any case
(4) block B will slide down if m1 > m2
2.
A wedge with a rough groove in the shape of a
quarter of a circle is kept on a smooth table (see
figure). A disc is placed in the groove with a small
clearance. Friction exists between groove and disc.
F
2Mg
(4) The minimum coefficient of friction required is
3F
2Mg
4.
3g . If
disc is to remain stationary relative to groove, the
coefficient of friction required can be.
For given situation select the Incorrect statement
The wedge is moved with an acceleration
(1) 1/3
(3) 1/5
(2) 1/4
(4) 9/10
(1) If µA > µB then contact force depends on mass
as well as angle of inclination of inclined plane.
(2) In every condition contact force depends on
mass and the inclination of the inclined plane
(3) If µA = µB then contact force between the
blocks is zero
(4) If µA = µB = 0 then contact force between them
will be zero
5.
In the system shown in figure the friction coefficient
between ground and bigger block is µ. There is no
friction between both the blocks. The string
connecting both the block is light, all three pulley
are light and frictionless. Then the minimum
2
6.
limiting value of µ so that the system remains in
equilibrium is:
assuming that man never slips on m 2 . (neglect the
(1) 1/2
(3) 2/3
(1) Projection velocity of ball with respect to
(2) 1/3
(4) 3/2
ground is 3iˆ + 10 ˆj + 5kˆ
A flexible chain of weight W hangs between two
fixed points A and B which are at the same
horizontal level. The inclination of the chain with
the horizontal at both the points of support is θ.
What is the tension of the chain at the mid point?
W
W
.tan 
.cos ec
(1)
(2)
2
2
W
.cot 
(3)
(4) None
2
Multiple Correct Type:
7.
A rope rests on two platforms, symmetrically both
inclined at angle q as shown in figure. Coefficient of
friction is 1 for the inclined surface.
(1) largest possible fractions of the rope that does
n
not touch the platform is
where n is
n +1
(sin cos – sin2)
(2) largest possible fractions of the rope that does
n
not touch the platform is
where n is
3+ n
(sin cos – sin2)
(3) Decreasing  would lead to smaller friction and
bigger hanging fraction.
(4) Decreasing  would result in smaller
requirement of friction for equilibrium.
8.
dimensions of system, and g = 10 m / s2 :
The system shown in figure is initially at origin and
is moving with velocity 5 m / skˆ . A force
(2) Z–co-ordinate of the point where ball lands is
25 m
(3) Relative motion between blocks start at t = 3
sec.
(4) Z–co-ordinate of the point where ball lands is
15 m
9.
A block of mass m is hanged at an angle  with line
of greatest slope on an incline of angle  as shown.
Minimum value of  for no sliping is, T is tension at
minimum .
sin  sin 
cos 
sin  cos 
(2) min =
cos 
(3) T = mg sin cos
(4) T = mg cos sin
(1) min =
10.
The arrangement shown in the diagram is moving
( )
with acceleration a = 4 ˆi + ˆj m/s2. An ideal spring
of natural length l0 having spring constant
K = 50 N/m is connected to block A. Blocks A and
B are connected by an ideal string passing through
F = (120t)iˆ acts on mass m 2 , [where F in newton, t
frictionless pulley. Mass of each block A and B is
in sec]. The man throws a light ball (at the instant
when m1 starts slipping on m 2 with a velocity
2 kg. If the friction coefficient between all the
10 m / s vertically up with respect to him self.
Taking the mass of each block and man as 60 kg and
(initially spring is in its natural length).
surfaces is 5/9 then just after releasing from rest,
3
(1)
(2)
(3)
(4)
11.
(1) Block loose contact from the plank before
relative motion starts between two blocks
(2) Block loose contact from the plank after the
starts of relative motion
(3) Relative motion between block and plank starts
10
at t = sec.
9
(4) Relative motion between block and plank starts
30
at t =
sec.
9
spring force is equal to tension in the string.
force exerted by the spring will be zero
the value of tension is close to 23.6 N
if  = 2/3 then spring force is zero
Imagine a situation in which the given arrangement
is placed inside an elevator that can move only in
the vertical direction and compare the situation with
the case when it is placed on the ground. When the
elevator accelerates downward with a0(< g).
Coefficient of friction between M and surface in
contact is µ while m is smooth, then (pulley and
Paragraph for Question 13 to 14
Figure shows two masses m1 = 10 kg and m2
connected by string passing over smooth fixed
pulleys. Mass m1 lies on a fixed rough surface
having a coefficient of friction µ = 0.8. The angle of
incline  = 37°.
string are ideal)
(1) the limiting friction force between the block M
and the surface decreases
(2) the system can accelerate with respect to the
elevator even when m < M
13.
The possible value(s) of m2 so that it remains at rest
is:
(1) 1 kg
(2) 5 kg
(3) 10 kg
(4) 15 kg
14.
For m2 = 12 kg and system is released from rest at
t = 1 s. Choose the correct statement(s):
(1) Speed of m1 at t = 1 s is zero.
(2) Speed of m1 at t = 2 s is zero.
(3) Speed of m1 as seen by m2 at t = 1 s is zero.
(4) Speed of m1 as seen by m2 at t = 2 s is zero.
(3) the system does not accelerate with respect to
the elevator unless m > M
(4) the tension in the string decreases
12.
A block of mass 1kg is placed over a long plank of
mass 3 kg. The friction coefficient between block
and plank is 0.5. The system is placed over a smooth
horizontal surface. A time varying force F = 5t
Newton starts acting on the block as shown in
figure. Select the Correct alternative:
Paragraph for Question 15 to 17
A block B of mass m is kept over a wedge A of
mass M as shown in the figure. Wedge is kept over a
frictionless horizontal surface.
4
Paragraph for Question 21 to 22
Block A of mass 5kg is on a plank of mass 10kg.
There is no friction between plank and ground but
coefficient of friction between block and plank is
0.4. Block is given velocity 18 m/s as shown in the
figure at t = 0.
15.
16.
The acceleration of wedge so that block does not
slip over the wedge is (assume friction between
block and wedge negligible)
(1) g cot
(2) g tan
M
m
g
g
(3)
(4)
M+m
m+M
If coefficient of friction between wedge and block is
, the maximum acceleration of the wedge so that
block does not slip over wedge is (tan > ).
  + tan  
 tan  −  
(1) 
 g (2) 
g
 1 −  tan  
 1 +  tan  
21.
After how much time relative motion stops between
block and plank:
(1) 4.5 sec
(2) 3 sec
(3) 6 sec
(4) 5 sec
22.
Minimum length of plank so that block does not fall
 mtan  + M 
 M − mtan  
(3) 
g
 g (4) 
 1 −  tan  
 1 +  tan  
17.
For the situation in question (12), minimum value of
acceleration is (tan > )
 M − mtan  
 M + mtan  
(1) 
 g (2) 
g
 1 +  tan  
 1 −  tan  
 tan  −  
(3) 
g
 1 +  tan  
  + tan  
(4) 
g
 1 −  tan  
off the plane:
(1) 27 m
(2) 36 m
(3) 18 m
(4) 24 m
Matrix Match Type:
23. In the shown diagram A is of mass 50 kg, B is of
mass 5 kg. Coefficient of friction between A and
ground is 0.2 and friction is absent between B and
ground. A horizontal force F is applied on B. f1 is
friction force between A and ground, a1 is
acceleration of A, a2 is acceleration of B.
Paragraph for Question 18 to 20
In diagram, the friction coefficient between the
block of mass 1 kg and the plank of mass 2 kg is 0.4
while that between the plank and floor is 0.1. A
constant force 'F' starts acting horizontally on the
upper 1 kg block.
18.
The acceleration of plank if F = 10 N is:
(1) 2.5 m/s2
(2) 1.5 m/s2
2
(3) 0.5 m/s
(4) 1.0 m/s2
19.
The friction force between plank and block if
F = 2 N, is:
(1) 3 N
(2) 4 N
(3) 2.5 N
(4) 2 N
(A)
(B)
(C)
(D)
24.
20.
For what value of F will the block move with double
the acceleration of that of the plank?
(1) 6 N
(2) 10 N
(3) 5 N
(4) 12.5 N
Column-I
F = 100 N
F = 125 N
F = 192.5 N
F = 80 N
Column-II
(P) f1 = 80 N
(Q) a1 = 0
(R) f1 = 125 N
(S) a1 = 1 m/s2
(T) a2 = 1 m/s2
All surfaces in contact have same value of friction
coefficients. Let frictional force between 2 kg and
6 kg be f1and between 6 kg and ground be f2.
(g = 10 ms–2)
5
Column-I
the force exerted on the bridge by the car when it is :
at the highest point of the bridge is (1200x) N. Find
x (Ignore air resistance and take g as 10 ms–2)
Column-II
(A) F = 36 N
(P)
f1 = 4 N, f2 = 32 N
(B)
F = 48 N
(Q)
f1 = 8 N, f2 = 32 N
(C)
F = 64 N
(R)
f1 = 10 N, f2 = 32 N
(D) F = 96 N
(S)
f1 = 0, f2 = 36 N
Numerical Grid Type:
25. Figure shows a ball of mass m connected with two
ideal springs of force constant k, kept in equilibrium
on a smooth incline, suddenly right spring is cut.
What is magnitude of instantaneous acceleration
(in m/s2) of ball.
28.
(
)
acceleration of B is.
29.
26.
In the figure shown the acceleration of A is,
aA = 15iˆ + 15 ˆj m / s 2 . If A is sliding on B then the
Figure shows a block placed on a bracket. Bracket is
placed unconstrained on a smooth floor, it is pulled
by a constant force F = 6i horizontally. Block is
projected with velocity v0 relative to bracket as
shown in figure. If time in second after which it
stops relative to bracket is t, then find the value of
0.6 t . Horizontal surface of bracket is smooth while
vertical surface is rough
(Given : m = 1 kg, M = 5 kg, v0 = 5 m/s,  = 0.5)
In the figure masses m1, m2 and M are 20 kg, 5kg
and 50 kg respectively. The co-efficient of friction
between M and ground is zero. The co-efficient of
friction between m1 and M and that between m2 and
ground is 0.3. The pulleys and the string are
massless. The string is perfectly horizontal between
P1 and m1 and also between P2 and m2. The string is
perfectly vertical between P1 and P2. An external
horizontal force F is applied to the mass M. Take
g = 10 m/s2.
(i)
Draw a free-body diagram for mass M, clearly
showing all the forces.
(ii) Let the magnitude of the force of friction
between m1 and M be f1 and that between m2
and ground be f2. For a particular F it is found
that f1 = 2f2. Find f1 and f2. Write down
equations of motion of all the masses. Find F,
tension in the string and accelerations of the
masses.
30.
27.
There is a parabolic-shaped bridge across a river of
width 100 m. The highest point of bridge is 5 m
above the level of the banks. A car of mass 1000 kg
is crossing the bridge at a constant speed of
20 ms–1.Using the notation indicated in the figure,
A 1 kg block B rests as shown on a bracket A of
same mass. Constant forces F1 = 20 N and F2 = 8 N
start to act at time t = 0 when the distance of block B
from pulley is 50 cm. Time when block B reaches
the pulley is
6
31.
The blocks are of mass 2 kg shown is in
equilibrium. At t = 0 right spring in figure (i) and
right string in figure (ii) breaks. Find the ratio of
instantaneous acceleration of blocks?
7
Answer Key
1. (3)
2. (4)
3. (1)
4. (2)
5. (3)
6. (3)
7. (1,4)
8. (1,2,3)
9. (1,3)
10. (2,3,4)
11. (1,3,4)
12. (2,3)
13. (1,2,3)
14. (1,2,3,4)
15. (2)
16. (1)
17. (3)
18. (3)
19. (4)
20. (3)
21. (2)
22. (1)
23. (A)-Q (B)-QR (C)-ST (D)-PQ
24. (A) S (B) P (C) Q (D) Q
25. (5)
26. (5)
27. (7)
28. ( –5iˆ m / s2 )
29.
30. (0.5)
31. (25/24)
PW Web/App - https://smart.link/7wwosivoicgd4
Library- https://smart.link/sdfez8ejd80if