First slide

Motion of block on Smooth incline

Question

A wedge Q of mass M is placed on a horizontal frictionless surface AB and a block P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination $θ$ , Q would slide by a distance of

Moderate

A

$(\frac{m}{M}) L cosθ$
B

$\frac{m}{L} (M + m)$
C

$\frac{(M + m)}{(mL \cos θ)}$
D

$\frac{(mL \cos θ)}{(m + M)}$

Solution

Let Q slides by a distance r towards left, then net horizontal displacement of P w.r.t. ground
= L cos $θ$ -x
Now apply $m_{1} x_{1} = m_{2} x_{2} \Rightarrow Mx = m (L cosθ - x)$
$\Rightarrow x = \frac{mL cosθ}{M + m}$

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