Question

A small block of mass $m$ is kept on a rough inclined surface of inclination $\theta$ fixed in an elevator. The elevator goes up with a uniform velocity $v$ and the block does not slide on the wedge. The work done by the force 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 $mgvt{\sin }^2\theta$

As block is not sliding

$f=mgsin\theta s=distancetravelled=vtw=Fscos\alpha \alpha isanglebetweenforceanddisplacementF=f=mgsin\theta \alpha =90-\theta w=mgsin\theta \times vt\times sin\theta w=mgvt{\sin }^2\theta$