Important questions based on NCERT syllabus for Chapter 5 - Law of Motion:
Question-1: A 30 kg boulder was initially moving at a velocity of 10 m/s, in order to stop it 10 N of constant retarding force is applied on it. After how long will the boulder stop?
Given, m = 30 kg.
Retarding force = -10N
u = 10 m/s
v = 0.
We know, F = ma
-10 = 30 x a
a = -1/3 ms^2
Also, v = u + at
0 = 10 – t/3
Therefore, t = -10 x (-3) = 30 s.
Question-2: Two billiard balls, each of mass 0.05 kg, moving in opposite directions with speed 6 ms-1 collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
Solution: Initial momentum of each ball before collision
= 0.05 x 6 kg ms-1 = 0.3 kg ms-1
Final momentum of each ball after collision
= – 0.05 x 6 kg ms-1 = – 0.3 kg ms-1 Impulse imparted to each ball due to the other
= final momentum – initial momentum = 0.3 kg m s-1 – 0.3 kg ms-1
= – 0.6 kg ms-1 = 0.6 kg ms-1 (in magnitude)
The two impulses are opposite in direction.
Question-3: A 0.2 kg bob which is hung to a hook by a 1m long string is pushed into oscillation. The velocity of the bob is 1 m/s at its mean position. What is the path of motion of the bob if we cut the string when the bob is at (1) one of its extreme positions, and (2) its mean position.
Solution: (1) When the bob is at either of its extreme point its velocity is zero. So if we cut the string now the bob will move vertically down under the influence of its weight.
(2) When the bob is at its mean position it has a horizontal velocity of2 m/s and upon cutting the string the bob will also experience the acceleration due to gravity. As a result the bob will behave like a projectile and trace a parabolic path to the floor.