DPP # 16 (FBD)

1. In the figure shown, a person wants to raise a block lying on the ground to a height h. In both
the cases if time required is same then in which case he has to exert more force. Assume
pulleys and strings light.

(i) (ii)
(A) (i) (B) (ii) (C) same in both (D) Cannot be determined
2. In the figure, at the free end of the light string, a force F is applied to keep the suspended mass
of 18 kg at rest. Then the force exerted by the ceiling on the system (assume that the string
segments are vertical and the pulleys are light and smooth) is: (g= 10 m/s2)
/////////////////////////////////////////////////

18kg

(A) 60 N (B) 120 N (C) 180 N (D) 240 N

3. A particle of mass m = 5kg, is momentarily at rest at x = 0 at t = 0. It is acted upon by two
forces F1 and . F2 It is given that F1 = 70 ĵ N and F2 is unknown. The particle experiences a
constant acceleration a , in the direction as shown. What third force, F3 , is required to make
the acceleration of the particle zero? (Note: sin = 4/5, cos = 3/5, and tan = 4/3. Neglect
gravity.)
y

→
F1 = 70 ĵ N
>

→ 2
a=10m/s


x

→
F2

(A) 30 ˆi + 40 ˆj (B) –( 30 ˆi + 40 ˆj ) (C) 40 ˆi + 30 ˆj (D) −(40 ˆi + 30 ˆj)

4. The block of mass ‘m’ equal to 100 kg is being pulled by a horizontal force
F = 2 mg applied to a string as shown in figure (Take g = 10 m/s2). The
pulley is massless and is fixed at the edge of an immovable table. What is
the value of force exerted by the supporting cable (rod) on the pulley (in
Newton)
(A) 3mg (B) 4mg (C) 2 2 mg (D) 2mg

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5. In which of the following cases the magnitude of acceleration of the block A will be maximum
(Neglect friction, mass of pulley and string)
m
m A
smooth A
(A) (B) (C) (D)
2mg B 2m
m A 2m m A 2mg

6. A weight W is supported by two strings inclined at 60º and 30º to the vertical. The tensions in
the strings are T1 & T2 as shown. If these tensions are to be determined in terms of W using a
triangle of forces, which of these triangles should you draw? (block is in equilibrium)
T2 T1

60° 30°

(A) (B) (C) (D) (E)

7. A frictionless wire is fixed between A and B inside a sphere of radius R. A bead slips along the
wire. The time taken by the bead to slip from A to B will be

2 gR 2 gR cos 
(A) 2 R / g (B) gR / gcos (C) (D)
gcos  g

8. Two weights W1 & W2 in equilibrium and at rest, are suspended as shown in figure. Then the
W1
ratio is :
W2

37°

W2
W1
(A) 5/4 (B) 4/5 (C) 8/5 (D) none of these
9. A uniform thick string of length 5 m is resting on a horizontal frictionless surface. It is pulled
by a horizontal force of 5 N from one end. The tension in the string at 1m from the force
applied is:

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 (A) zero (B) 5 N (C) 4 N (D) 1 N
10. A body of mass 1 kg lies on smooth inclined plane. The block of mass m is given force F = 10
N horizontally as shown. The magnitude of net normal reaction on the block is: (g = 10m/s2)

F=10N
45°

10
(A) 10 2 N (B) N (C) 10 N (D) none of these
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DPP # 17 (EQUATION)
1. A heavy particle of mass 1kg is suspended from a massless string attached to a roof. A
horizontal force F is applied to the particle such that in the equilibrium position the string
makes an angle 300 with the vertical. The magnitude of the force F equals

10
(A) 10 N (B) 10 3 N (C) 5 N (D) N
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2. Two blocks A and B of masses 4 kg and 8 kg respectively are placed on a smooth plane
surface. A force F of 12 N is applied on A as shown. Find the force of contact (in N) between A
and B?

(A) 8 N (B) 6 N (C) 10 N (D) None of these

3. Ideal Pulleys A, B, C are connected to the mass as shown in figure. Tension in the rope
connecting A to the wall is :

(A) m g (B) 4 m g (C) 8 m g (D) none of these

4. In the figure (i) an extensible string is fixed at one end and the other end is pulled by a tension
T. In figure (ii) another identical string is pulled by tension 'T' at both the ends. The ratio of
elongation in equilibrium of string in (i) to the elongation of string in (ii) is

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 (A) 1 : 1 (B) 1 : 2 (C) 2 : 1 (D) 0
5. As shown in figure, mass M = 10 gms is placed on an inclined plane. In order to keep it at rest
the value of m will be-

M m

30°

(A) 5 gm (B) 10 3 gm (C) 0.10 gm (D) 1.0 3 gm

6. Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in
natural length. Find out the accelerations of blocks A and B respectively just after release
(pulley, string and spring are massless).
//////////////////////////////

Spring
k

m A B 2m

g g
(A) g , g  (B)   (C) 0, 0 (D) g  0
3 3
7. The engine of a car produces acceleration 4 m/s2 in the car. If this car pulls another car of same
mass. What will be the acceleration produced-
(A) 1 m/s2 (B) 1.5 m/s2 (C) 2 m/s2 (D) 4 m/s2
8. A uniform thick rope of length 5m is kept on frictionless surface and a force of 5N is applied to
one of its end. Find tension in the rope at 1m from this end-
(A) 1N (B) 3N (C) 4N (D) 5N
9. A force 10 N acts on a body of mass 20 kg for 10 sec. Change in its momentum is-
(A) 5 kg m/s (B) 100 kg m/s (C) 200 kg m/s (D) 1000 kg m/s
10. Three blocks of masses m1, m2 and m3 are connected by
massless strings as shown on a frictionless table. They
are pulled with a force T3 = 40 N. If m1 = 10 kg, m2 = 6
kg and m3 = 4 kg, the tension T2 will be-
(A) 20 N (B) 40 N (C) 10 N (D) 32 N
11. A light string passes over a frictionless pulley. To one of its ends a mass of 6 kg is attached and
to its other end a mass of 10 kg is attached. The tension in the string will be -

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 6kg
10kg

(A) 50 N (B) 75 N (C) 100 N (D) 150 N

12. A force of 5 Newton acts horizontally on a body of weight 9.8 Newton. What is the
acceleration produced in m s–2 ? (g = 9.8 m/s2)
(A) 0.51 (B) 1.46 (C) 49.00 (D) 5.00
13. In the shown mass pulley system, pulleys and string are massless. The one end of the string is
pulled by the force F = 2mg. The acceleration of the block will be

(A) g/2 (B) 0 (C) g (D) 3g

DPP # 18 (TIPICAL PROBLEMS)
1. The velocities of A and B are shown in the figure. Find the speed (in ms –1) of block C.(Assume
that the pulleys and string are ideal.

(A) 1 (B) 2 (C) zero (D) 2

2. Two men of masses m and m/2 starts climbing up on two massless strings fixed at the ceiling
with acceleration g and g/2 respectively. The ratio of tensions in the two strings will be :
(A) 2 : 1 (B) 4 : 1 (C) 4 : 3 (D) 8 : 3
3. Consider the system as shown in the figure. The pulley and the string are light and all the
surfaces are frictionless. The tension in the string is (g = 10 m/s2).

1kg
horizontal surface

1kg
(A) 0 N (B) 1 N (C) 2 N (D) 5 N
4. For the system shown in figure, the tension in the string is T (inclined surfaces are frictionless).
m
mass is shifted from A to B or B to A as per given in options. Then :
2

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 (A) Tension in the string will increase when mass is shifted from A to B.
(B) Tension in the string will increase when mass is shifted from B to A.
(C) acceleration of blocks will increase when mass is shifted from A to B.
(D) acceleration of blocks will increase when mass is shifted from B to A.
5. A cart of mass 0.5 kg is placed on a smooth surface and is connected by a string to a block of
mass 0.2 kg. At the initial moment the cart moves to the left along a horizontal plane at a speed
of 7 m/s.
(Use g = 9.8 m/s2)

0.5 kg

0.2 kg
2g
(A) The acceleration of the cart is towards right.
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(B) The cart comes to momentary rest after 2.5 s.
(C) The distance travelled by the cart in the first 5s is 17.5 m.
(D) The velocity of the cart after 5s will be same as initial velocity.

6. A block of mass M1 = 3 kg on a smooth fixed inclined plane of angle 300 is connected by a

cord over a small frictionless pulley to a second block of mass 2 kg hanging vertically. The
tension T in the cord and the acceleration a of the blocks are :

(A) a = 1m/s2 (B) a = 2m/s2, (C) T = 9 N (D) T = 18N

7. Three blocks are connected by light strings as shown in figure and pulled by a force F = 60 N.
If mA = 10 kg, mB = 20 kg and mC = 30 kg, then :

(A) acceleration of the system is 2 m/s2 (B) T1 = 10 N

(C) T2 = 30 N (D) T1 = 20 N & T2 = 40 N
8. Find the acceleration of blocks in Fig. the pulley and the strings are mass less :

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 F
(A) The acceleration of block of mass M is A =
M + 4m
2F
(B) The acceleration of block of mass m is a=
(M + 4m)
2F
(C) The acceleration of block of mass M is A =
M + 4m
4F
(D) The acceleration of block of mass m is a=
(M + 4m)
9. A uniform sphere of weight 'w' and radius 3m is being held by a string of 2m
length 2m. attached to a frictionless wall as shown in the figure. Wall
(A) Tension in the string will be 5w/4.
(B) Tension in the string will be 3w/4.
(C) Normal reaction by the wall on the sphere will be 3w/4.
(D) Normal reaction by the wall on the sphere will be 5w/4.

10. In the system shown in figure wedge is fixed. All the contact surfaces are frictionless. All the
pulleys are light and strings are light and inextensible. Then : [ Take g = 10 m/s2]

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(A) Magnitude of acceleration of the each block is m/s2.
6
 130 
(B) Tension in the string connecting block A and block B is   N.
 3 
55
(C) Tension in the string connecting block B and block C is N.
3
55
(D) Force exerted by string on pulley Q is N.
3

11. A wedge of mass M is pushed with an constant acceleration of a = gtan along a smooth
horizontal surface and a block of mass m is projected down the smooth incline of the wedge
with a velocity V relative to the wedge.

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 L
(A) The time taken by the block to cover distance L on the incline plane is
V
2L
(B) The time taken by the block to cover distance L on the incline plane is
g sin 
(C) The normal reaction between the block and wedge is mg sec
(D) The horizontal force applied on the wedge to produce acceleration a is (M + m) g tan.

12. Match the following:

Three blocks of masses m1, m2 and M are arranged as shown in figure. All the surfaces are
frictionless and string is inextensible. Pulleys are light. A constant force F is applied on block
of mass m1. Pulleys and string are light. Part of the string connecting both pulleys is vertical
and part of the strings connecting pulleys with masses m1 and m2 are horizontal.

F
(P) Acceleration of mass m1 (1)
m1
F
(Q) Acceleration of mass m2 (2)
m1 + m2
(R) Acceleration of mass M (3) zero
m2F
(S) Tension in the string (4)
m1 + m2
(A) P-1, Q-1, R-1,S-3 (B) P-2, Q-2, R-3,S-4
(C) P-2, Q-4, R-3,S-1 (D) P-2, Q-2, R-3,S-3

DPP # 19(FRICTION)
1. A force F accelerates a block of mass m1. The coefficient of friction between the contact
surfaces is . The acceleration of m1 will be:

F − 2 m1 g m1 +m2
(A)  g − (B)
m1 + m2 F−2m1g

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 F − 2m1g
(C) − g (D) F − (m1 + m2) g
m1 + m 2

2. In the shown arrangement if f1, f2 and T be the frictional forces on 2 kg block, 3kg block &
tension in the string respectively, then their values are:
(A) 2 N, 6 N, 3.2 N
(B) 2 N, 6 N, 0 N
(C) 1 N, 6 N, 2 N
(D) data insufficient to calculate the required values.

3. With reference to the figure shown, if the coefficient of friction at all the surfaces is 0.42, then
the force required to pull out the 6.0 kg block with an acceleration of 1.50 m/s2 will be:

(A) 36 N (B) 24 N (C) 84 N (D) 51 N

4. A block is placed on an inclined plane and has to be pushed down. The angle of inclination of
the plane is:
(A) equal to angle of repose (B) more than angle of repose
(C) less than the angle of repose (D) equal to angle of friction

5. In the figure mA = mB = mC = 60 kg. The co-efficient of friction between C and ground is 0.5, B
and ground is 0.3, A & B is 0.4. C is pulling the string with the maximum possible force
without moving. Then tension in the string connected to A will be:

(A) 120 N (B) 60 N (C) 100 N (D) zero

6. Figure shows a system of two blocks of 10 kg and 5 kg mass, connected by ideal strings and
pulleys. Here ground is smooth and friction coefficient between the two blocks is µ = 0.5. A
horizontal force F is applied on lower block as shown. The minimum value of F required to
start sliding between the blocks is : (Tage g = 10 m/s2)

(A) 12.5 N (B) 25 N (C) 50 N (D) 100 N

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7. Two blocks of masses 5 kg and 3kg are placed in contact over an inclined surface of angle 37°,
as shown. µ1 is friction coefficient between 5kg block and the surface of the incline and
similarly, µ2 is friction coefficient between the 3kg block and the surface of the incline. After
the release of the blocks from the inclined surface,
3kg
5kg µ2
µ1
37°

(A) if µ1 = 0.5 and µ2 = 0.3 then 5 kg block exerts 3N force on the 3 kg block
(B) if µ1 = 0.5 and µ2 = 0.3 then 5 kg block exters 8 N force on the 3 kg block
(C) if µ1 = 0.3 and µ2 = 0.5 then 5 kg block exerts 1 N force on the 3kg block.
(D) if µ1 = 0.3 and µ2 = 0.5 then 5 kg block exerts no force on the 3kg block.

8. A 20 kg block is initially at rest. A minimum of 80 N horizontal force is required to set the

block in motion. After the motion, a horizontal force of 60 N is applied to keep the block
moving with constant speed. The coefficient of static friction and kinetic friction is-
(A) k = 0.3 (B) s = 0.3 (C) k = 0.4 (D) s = 0.4
9. All the blocks shown in the figure are at rest. The pulley is smooth and the strings are light.
Coefficient of friction at all the contacts is 0.2. A frictional force of 10 N acts between A and
B.The block A is about to slide on block B.The normal reaction and A
frictional force exerted by the ground on the block B is.
(A)The normal reaction exerted by the ground on the block B is 110N C 5 kg
(B)The normal reaction exerted by the ground on the block B is 50 N
(C) the frictional force exerted by the ground on the block B is 20N
B
(D) the frictional force exerted by the ground on the block B is zero

10. A wedge is moving rightwards on which a block of mass 10kg is placed on it. Friction
coefficient between the wedge and the block is 0.8. [take g = 10 m/s2]. Select correct
alternative(s) among the following options.

(A) If wedge is moving with constant velocity then friction acting on block is 64N.
(B) If wedge is moving with constant velocity then acceleration of block is zero.
(C) If wedge is moving with = 2 ( î ) m/s2 then friction acting on block is 44N.
(D) If wedge is moving with = 10 ( î ) m/s2 then friction is 20N, downward on the wedge along
the inclined.

DPP # 20 (friction)
1. A lift is moving downwards with an acceleration equal to the acceleration due to gravity. A
body of mass M kept on the floor of the lift is pulled horizontally, if the coefficient of friction is
µ, then the frictional resistance offered by the body is

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 (A) Mg (B) µMg (C) 2µMg (D) zero 'kwU;

2. A block of metal is lying on the floor of a bus. The maximum acceleration which can be given
to the bus so that the block may remain at rest, will be-
(A) µg (B) 2 µg (C) µ2g (D) µg2

3. A 60 kg body is pushed horizontally with just enough force to start it moving across a floor and
the same force continues to act afterwards. The coefficient of static friction and sliding friction
are 0.5 and 0.4 respectively. The acceleration of the body is :
(A) 6 m/s2 (B) 4.9 m/s2 (C) 3.92 m/s2 (D) 1 m/s2

4. Both the blocks shown in the given arrangement are given together a horizontal velocity
towards right. If acm be the subsequent acceleration of the centre of mass of the system of
blocks, then acm equals (before sliding stops at all surfaces) :

(A) 0 m/s2 (B) 5/3 m/s2 (C) 7/3 m/s2 (D) 2 m/s2
5. A block B is pushed momentarily along a horizontal surface with an initial velocity v. If  is
the coefficient of sliding friction between B and the surface, block B will come to rest after a
time :

v g g v
(A) (B) (C) (D)
g v v g

6. The coefficient of friction between the block and the horizontal surface is µ. The block moves
towards right under action of horizontal force F(figure -a). Sometime later another force P is
applied to the block making an angle  (such that tan = m) with vertical as shown in (figure -
b). After application of force P, the acceleration of block shall

(A) increase (B) decrease

(C) remains same (D) information insufficient for drawing inference.
7. If the coefficient of friction between A and B is , the maximum horizontal acceleration of the
wedge A for which B will remain at rest w.r.t the wedge is :

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  1+   g 1–  
(A)  g (B) g  (C) (D) g 
 1–     1+  

8. In the arrangement shown, W1 = 200 N, W2 = 100 N,  = 0.25 for all B

surfaces in contact. The block W1 just slides under the block W2.
(A) A pull of 50 N is to be applied on W1 A
(B) A pull of 90 N is to be applied on W1 W2 45°
P
(C) Tension in the string AB is 10 N W1
(D) Tension in the string AB is 20N

9. Two block A and B placed on plane surface as shown in the figure. The mass of block A is 100
kg and that of block B is 200 kg. Block A is tied to a stand and block B is pulled by a force F.
If the coefficient of friction between the surfaces of A and B is 0.2 and the coefficient of
friction between B and the plane is 0.3 then for the motion of B the minimum value of F will
be-

A
F
B

(A) 700 N (B) 1050 N (C) 900 N (D) 1100 N

10. Two blocks of mass m and 2m are slowly just placed in contact with each other on a rough
fixed inclined plane as shown.Initially both the blocks are at rest on inclined plane. The
coefficient of friction between either block and inclined surface is . There is no friction
between both the blocks. Neglect the tendency of rotation of blocks on the inclined surface.
Column I gives four situations. Column II gives condition under which statements in column I
are true. Match the statements in column I with corresponding conditions in column II.

Column I Column II
(A) The magnitude of acceleration of both blocks are same if (p)  = 0
(B) The normal reaction between both the blocks is zero if (q)  > 0
(C) The net reaction exerted by inclined surface on each (r)  > tan
block make same angle with inclined surface (AB) if
(D) The net reaction exerted by inclined surface on block (s)  < tan
of mass 2m is double that of net reaction exerted by
inclined surface on block of mass m if

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 ANSWER KEY
DPP – 16
1. A 2. D 3. B 4. C 5. C 6. E 7. A
8. A 9. C 10. A

DPP – 17
1. D 2. A 3. C 4. A 5. A 6. A 7. C
8. C 9. B 10. D 11. B 12. D 13. D
DPP – 18
1. A 2. D 3. D 4. BC 5. ABC 6. AD 7. BC
8. AB 9. AC 10. ABCD 11. ACD 12. B

DPP – 19
1. C 2. C 3. D 4. C 5. D 6. B 7. AD
8. AD 9. AD 10. BCD

DPP – 20
1. D 2. A 3. D 4. D 5. A 6. C 7. B
8. BD 9. D 10. (A) p,q,r,s (B) p,q,r,s, (C) p,q,r,s, (D) p,q,r,s

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