A block of mass 'm' is initially lying on a wedge of mass 'M' with an angle of

Question

A block of mass 'm' is initially lying on a wedge of mass 'M' with an angle of inclination

θ

, as shown in the figure. Calculate the displacement of the wedge when the block reaches bottom of the wedge.

Options:

A . mhM+m

B . mhcotθM+m

C . mhcosθM+m

D . mhsinθM+m

Answer: Option B
:
B

l = h c o s θ

Let displacement of wedge be x towards right:

Δ x_{C M} = \frac{m (l + x) + M x}{M + m}

0 = m l + (M + m) x

x = \frac{- m l}{M + m} = - \frac{m h c o t θ}{M + m}

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