Question

A block of mass m is resting on a wedge of mass M and inclination $\theta .$ Wedge is accelerated with $a=gtan\theta$ as shown in figure. The acceleration of block with respect to wedge is (assume all surfaces to be smooth)

• A. zero
• B. $2gsin\theta$
• C. $gsin\theta (1-tan\theta )$
• D. $gsin\theta (1+tan\theta )$

Answer 1

The correct option is B $2gsin\theta$

Drawing FBD of block m from the frame of wedge,

let $a_0$ is acceleration of block with respect of wedge,

$m{a}_0=macos\theta +mgsin\theta$

$a_0=gtan\theta cos\theta +gsin\theta$

$a_0=2gsin\theta$