Question

A smooth block of mass $m$ moves up from bottom to top of a wedge which is moving with an acceleration $a_0$ Find the work done by the pseudo force measured by the person sitting at the edge of the wedge.

Diagram

• A. $m{a}_0\sqrt{l+b}$
• B. $m{a}_{0}l$
• C. $m{a}_0\sqrt{l^2+b^2}$
• D. $m{a}_{0}l\frac{b}{\sqrt{l^2+b^2}}$

Answer 1

The correct option is B $m{a}_{0}l$

As given wedge is moving with constant acceleration $a_0$, so pseudo force will act on the block.
So, pseudo force,

$\overrightarrow{F_{ps}}=-m\overrightarrow{a_0}=-m\left(a_0\hat{i}\right)$
is a constant force.

Work done by pseudo force,

$W_{ps}=\overrightarrow{F_{ps}}.\overrightarrow{S}$

$W_{ps}=-m\left(a_0\hat{i}\right).(-l\hat{i}+b\hat{j})$

$W_{ps}=m{a}_{0}l$