Question

A small block of mass $m$ is kept on a rough inclined surface of inclination $\theta$ fixed in a elevator. The elevator goes down with a uniform velocity $v$ and the block does not slide on the wedge . The work done by the following of friction on the block in time $t$ will be

• A. $zero$
• B. $-mgvt{\cos }^2\theta$
• C. $-mgvt{\sin }^2\theta$
• D. $mgvt\sin 2\theta$

Answer 1

The correct option is C $-mgvt{\sin }^2\theta$

$F_{block}=mgsin\theta$ (along the inclined surface)
velocity component acting on the block along friction= $vsin\theta$
$S=vsin\theta t$
$W=mgvtsi{n}^2\theta$ will be the work done by the block
$W_{fr}=-mgvtsi{n}^2\theta$