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

Options

A. `((m)/(M)) L cos theta`
B. `(m)/(L) (M + m)`
C. `((M + m))/((mL cos theta))`
D. `((mL cos theta))/((m + M))`

Answer

D

Explanation

(d) Let `Q` slides by a distance `x` towards left, then net horizontal displacement of `P` w.r.t. ground
=`L cos theta - x`
Now apply `m_1 x_1 = m_2 x_2 rArr Mx = m (L cos theta - x)`
`rArr x = (mL cos theta)/(M + m)`.