Chapter 3
Laws of Motion
Solutions
SECTION - A
Objective Type Questions (One option is correct)
[Laws of Motion]
1. A uniform rod is held at rest against a rough wall and a rough floor. Which of the following represents correct
free body diagram of rod? (All standard symbols used)
m
f2 f2
N2 f2
N2 N2
N2
(1) f2 N1 (2) (3) N1 (4)
N1 N1
mg mg mg
f1 mg
f1 f1 f1
Sol. Answer (3)
mg, downwards, normal perpendicular to the contacts and frictional forces opposite to tendency of motion.
2. Force is applied on an object of mass 2 kg at rest on a frictionless horizontal surface as shown in the graph.
The speed of object at t = 1 s will be
F(N)
20
10
t(s)
5 10
(1) 7.5 m/s (2) 12.5 m/s (3) 10 m/s (4) 25 m/s
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,50 Laws of Motion Solutions of Assignment
Sol. Answer (3)
At 0 to 1s
Area = 20 = p = 2 (v – 0) v = 10 m/s
3. When a lift is moving upward with acceleration of 5 m/s2 then percentage change in the weight of the person
in the lift is x%. If the lift is moving down with acceleration 5 m/s2 then percentage change in the weight of
same person is y%. Then the ratio x is (g = 10 m/s2)
y
(1) 1 : 1 (2) 3 : 1 (3) 1 : 3 (4) 3 : 4
Sol. Answer (1)
In first condition, weight of person w = m (g + 5) = 15 m
5m
x= 100 50% increase
10 m
⎧ 5 m 10 m ⎫
Similarly y = ⎨ ⎬ = 50% decrease
⎩ 10 m ⎭
x
y = 1 :1
4. A block of mass 2 kg rests on the floor of an elevator, which is moving down with an acceleration ‘g’, then the
apparent weight of the block is
[take g = 10 m/s2]
(1) 20 N (2) 12 N (3) 16 N (4) Zero
Sol. Answer (4)
N=0
Since body is freely falling
5. Swimming is possible on account of
(1) First law of motion (2) Second law of motion
(3) Third law of motion (4) Newton's law of gravitation
Sol. Answer (3)
Action and reaction pair.
6. When we jump out a boat standing in river water it moves
(1) Backward (2) Forward (3) Sideways (4) None of these
Sol. Answer (1)
Action and reaction pair
7. Ram is on a frictionless horizontal plane. How can Ram get off if no horizontal force is exerted by pushing
against the surface?
(1) By jumping (2) By spitting or sneezing
(3) By rolling Ram's body on the surface (4) By running on the plane
Sol. Answer (2)
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,Solutions of Assignment Laws of Motion 51
8. A block of mass 5 kg is placed on a smooth table and tied from both ends by two masses 3 kg and
2 kg by means of light, inextensible strings passing through pulleys as shown. The tension in the string connecting
5 kg and 3 kg is (g = 10 m/s2)
5 kg
2 kg 3 kg
(1) 22 N (2) 27 N (3) 33 N (4) 30 N
Sol. Answer (2)
Acceleration of the system is given as
T1 T
3g – 2g = (3 + 2 + 5) a 5 kg
g
a=
10 T1 T
2 kg
Now 3g – T = 3a
3g
T = 3g – = 2.7g = 27 N
10
9. A block is placed on a smooth inclined plane as shown. For what value of horizontal force F, the block will
remain at rest?
F
m
(1) mg tan (2) mg sin (3) mg cos (4) mg cot
Sol. Answer (1) F cos
To keep the block at rest F
m
F sin
F cos = mg sin mg sin
F = mg tan
10. Figure shows a small ball of mass m held at rest by means of two light and inextensible strings. The
tensions in the inclined string at the instant shown and just after cutting the horizontal string are
respectively
m
Scissor
mg mg mg mg
(1) mg cos , mg cos (2) mg cos , (3) , mg cos (4) ,
cos cos cos cos
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, 52 Laws of Motion Solutions of Assignment
Sol. Answer (3)
Before cutting,
T cos = mg
mg
T
cos
and just after the cutting, ball moves freely on circular path.
hence T = mg cos {As v 0}
T
mg sin
mg cos mg
11. In the arrangement shown, what is the normal reaction between the block A (mass = 5 kg) and ground
A 2 kg
5 kg
(1) 50 N (2) 20 N (3) 30 N (4) Zero
Sol. Answer (3)
N = 30 N
12. If pulley and all strings as shown are massless, then tension T2 = 100 N. Calculate weight of the block (g =
10 m/s2)
60° 30°
T1 T2
(1) 50 N (2) 100 N (3) 50 3 N (4) 100 3 N
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Laws of Motion
Solutions
SECTION - A
Objective Type Questions (One option is correct)
[Laws of Motion]
1. A uniform rod is held at rest against a rough wall and a rough floor. Which of the following represents correct
free body diagram of rod? (All standard symbols used)
m
f2 f2
N2 f2
N2 N2
N2
(1) f2 N1 (2) (3) N1 (4)
N1 N1
mg mg mg
f1 mg
f1 f1 f1
Sol. Answer (3)
mg, downwards, normal perpendicular to the contacts and frictional forces opposite to tendency of motion.
2. Force is applied on an object of mass 2 kg at rest on a frictionless horizontal surface as shown in the graph.
The speed of object at t = 1 s will be
F(N)
20
10
t(s)
5 10
(1) 7.5 m/s (2) 12.5 m/s (3) 10 m/s (4) 25 m/s
Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456
,50 Laws of Motion Solutions of Assignment
Sol. Answer (3)
At 0 to 1s
Area = 20 = p = 2 (v – 0) v = 10 m/s
3. When a lift is moving upward with acceleration of 5 m/s2 then percentage change in the weight of the person
in the lift is x%. If the lift is moving down with acceleration 5 m/s2 then percentage change in the weight of
same person is y%. Then the ratio x is (g = 10 m/s2)
y
(1) 1 : 1 (2) 3 : 1 (3) 1 : 3 (4) 3 : 4
Sol. Answer (1)
In first condition, weight of person w = m (g + 5) = 15 m
5m
x= 100 50% increase
10 m
⎧ 5 m 10 m ⎫
Similarly y = ⎨ ⎬ = 50% decrease
⎩ 10 m ⎭
x
y = 1 :1
4. A block of mass 2 kg rests on the floor of an elevator, which is moving down with an acceleration ‘g’, then the
apparent weight of the block is
[take g = 10 m/s2]
(1) 20 N (2) 12 N (3) 16 N (4) Zero
Sol. Answer (4)
N=0
Since body is freely falling
5. Swimming is possible on account of
(1) First law of motion (2) Second law of motion
(3) Third law of motion (4) Newton's law of gravitation
Sol. Answer (3)
Action and reaction pair.
6. When we jump out a boat standing in river water it moves
(1) Backward (2) Forward (3) Sideways (4) None of these
Sol. Answer (1)
Action and reaction pair
7. Ram is on a frictionless horizontal plane. How can Ram get off if no horizontal force is exerted by pushing
against the surface?
(1) By jumping (2) By spitting or sneezing
(3) By rolling Ram's body on the surface (4) By running on the plane
Sol. Answer (2)
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,Solutions of Assignment Laws of Motion 51
8. A block of mass 5 kg is placed on a smooth table and tied from both ends by two masses 3 kg and
2 kg by means of light, inextensible strings passing through pulleys as shown. The tension in the string connecting
5 kg and 3 kg is (g = 10 m/s2)
5 kg
2 kg 3 kg
(1) 22 N (2) 27 N (3) 33 N (4) 30 N
Sol. Answer (2)
Acceleration of the system is given as
T1 T
3g – 2g = (3 + 2 + 5) a 5 kg
g
a=
10 T1 T
2 kg
Now 3g – T = 3a
3g
T = 3g – = 2.7g = 27 N
10
9. A block is placed on a smooth inclined plane as shown. For what value of horizontal force F, the block will
remain at rest?
F
m
(1) mg tan (2) mg sin (3) mg cos (4) mg cot
Sol. Answer (1) F cos
To keep the block at rest F
m
F sin
F cos = mg sin mg sin
F = mg tan
10. Figure shows a small ball of mass m held at rest by means of two light and inextensible strings. The
tensions in the inclined string at the instant shown and just after cutting the horizontal string are
respectively
m
Scissor
mg mg mg mg
(1) mg cos , mg cos (2) mg cos , (3) , mg cos (4) ,
cos cos cos cos
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, 52 Laws of Motion Solutions of Assignment
Sol. Answer (3)
Before cutting,
T cos = mg
mg
T
cos
and just after the cutting, ball moves freely on circular path.
hence T = mg cos {As v 0}
T
mg sin
mg cos mg
11. In the arrangement shown, what is the normal reaction between the block A (mass = 5 kg) and ground
A 2 kg
5 kg
(1) 50 N (2) 20 N (3) 30 N (4) Zero
Sol. Answer (3)
N = 30 N
12. If pulley and all strings as shown are massless, then tension T2 = 100 N. Calculate weight of the block (g =
10 m/s2)
60° 30°
T1 T2
(1) 50 N (2) 100 N (3) 50 3 N (4) 100 3 N
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