Question

A block of mass $m$ is placed on an inclined plane which is moving with constant velocity $v$ in horizontal direction as shown in figure. Then find out work done in ground frame by the friction in time $t$, if the block is at rest with respect to the inclined plane.

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

Answer 1

The correct option is A $-mgvt\sin \theta \cos \theta$

F.B.D of block with respect to ground.


Block is at rest with respect to wedge
$\Rightarrow f=mg\sin \theta$
In time $t$ the displacement of block with respect to ground $d=vt$

Work done by friction with respect to man $A$
$W_f=$ (Component of friction force along displacement) $\cdot$ Displacement
$W_f=\left(mg\sin \theta \cos \right({180}^{\circ }-\theta \left)\right)\cdot vt$
$W_f=-mgvt\cos \theta \sin \theta$