Question

A block is projected up on a rough inclined plane which is fixed. Mass of black is $m$ & initial speed is $v_o$. If the block stops after sometime, now which of the statement is correct regarding work done by friction?

• A. It is negative & equal to $\frac{1}{2}m{v}_o^2$.
• B. It is negative on block but positive on inclined plane.
• C. Total work done by friction on the system is zero.
• D. The work done by friction on block is less then $\frac{1}{2}m{v}_o^2$ & on inclined plane is zero.

Answer 1

The correct option is D The work done by friction on block is less then $\frac{1}{2}m{v}_o^2$ & on inclined plane is zero.

Using Work-Energy Theorem, we can say:
Work done on block $=\Delta K.E.$

Work done by $mg$ and friction will be negative in nature, because both are opposite to the direction of displacement.

$-W_{grav}-W_{friction}=K.E{.}_f-K.E{.}_i{W}_{grav}+W_{friction}=\frac{1}{2}m{v}_0^2$

$W_{friction}=\frac{1}{2}m{v}_0^2-W_{grav}$

As, the magnitude of work done by gravity will be certain positive value, we can say that, $W_{friction}<\frac{1}{2}m{v}_0^2$.