Question

A block of mass m is kept on a wedge of mass M. Initially the system is held. At certain time the system is released and the wedge is observed to move with acceleration A on inclined surface as shown. There is no friction anywhere. The acceleration of block (m) with respect to wedge (M) will be

• A. A rightward
• B. $Acos\theta +gsin\theta$ rightward
• C. $Acos\theta +gsin\theta$ leftward
• D. None of these

Answer 1

The correct option is B $Acos\theta +gsin\theta$ rightward

Given,

Mass of wedge$=$M

Mass of block$=$m

Angle of inclination$=\theta$

Acceleration of wedge after released$=$A

FBD of block wr to wedge

Let N is constant force b/w block and wedge

There is not reletive acceleration along the common normal

Resultant force along the incline plane

$f=mA\cos \theta +mg\sin \theta$

$m{a}_r=mA\cos \theta +mg\sin \theta$

$a_r=A\cos \theta +g\sin \theta$

Block will move along the inclination with respect to wedge with acceleration $a_r=A\cos \theta +g\sin \theta$.