Let h 0 be the initial height of ball with respect to the earth. The coefficient of restitution is e.
Column-I | Column-II |
(i) Total distance travelled by the ball before coming to rest | [A] e2n h0 |
(ii) Height attained after n impacts | [B] b h0 |
(iii) Average force exerted by ball | [C] P |
(iv) Total momentum transferred to the earth | [D] mg |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)-[B], (ii)-[A], (iii)-[D], (iv)-[C]
Sol. From definition of coefficient of restitution
e = 
= 
= 
(h 1 = height attained after impact, h 0 = Drop height)
h 1 = e 2 h 0
After n impact / collision
h n = e 2n h 0
So 
(P)
Total distance travelled by the ball before coming to rest.
h = h 0 + 2h 1 + 2h 2 + …
h = h 0 + 2e 2 h 0 + 2e 4 h 0 + …
= h 0 (1 + e 2 ) (1 – e 2 ) –1 h = h 0 
So 
(Q)
P 1 = P – (– eP) = P (1 + e)
P 2 = eP (1 + e)
Total momentum transfer is
P = P (1 + e) + eP (1 + e) + …
= P 
So 
(R)
Average force F = 
= 
= mg
So 
(S)
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