Question

A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ₀. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ₁. Then M is given by :
(A) (m/2) [(θ₀ + θ₁)/(θ₀ - θ₁)]

(B) m [(θ₀ - θ₁)/(θ₀ + θ₁)]

(C) m [(θ₀ + θ₁)/(θ₀ - θ₁)]
(D) (m/2) [(θ₀ - θ₁)/(θ₀ + θ₁)]

Answer 1

Thus the value of M is given by M =  ​θ o  − θ  1  / θo + θ 1  x m

Option (B) is correct.

Explanation:

u = √ 2gl( 1 − cosθo  )   ........ (1)

v = velocity of ball after collision

v =  m−M  / m+M  x u

Since ball rises up to height θ1.

v = √ 2gl( 1 − cosθo  )  = m−M  / m+M  x u ---- (2)

From (1) and (2)    m−M  / m+M  = 1 −cosθ  1 − cosθo = Sin θ  1 / 2 ÷ sin θ  / 2

M / m  =  ​θ o  −θ  1  / θo  + θ  1

M =  ​θ o  − θ  1  / θo  + θ  1  x m

Thus the value of M is given by M =  ​θ o −θ  1  / θo  + θ  1  x m

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