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 :

The correct option is D m(θ₀−θ₁)/(θ₀+θ₁)
u=√2gl(1−cosθ₀) (1)
v= velocity of ball after collision
v=(m−M)/(m+M)u
Since ball rises upto height θ₁
v=√2gl(1−cosθ₁)=(m−M)/(m+M)u. (2)
From (1) and (2)
(m−M)/(m+M)=√(1−cosθ₁)/√(1−cosθ₀)
=sin(θ₁/2)/sin(θ₀/2)
Assuming θ₀ and θ₁ are small angles,
(m−M)/(m+M) = θ₁/2 / θ₀/2 = θ₁/θ₀
m−M = mθ₁/θ₀ − Mθ₁/θ₀
mθ₀ − Mθ₀ = mθ₁ − Mθ₁
m(θ₀ − θ₁) = M(θ₀ − θ₁)
M = m(θ₀−θ₁)/(θ₀+θ₁)