Question

A coconut of mass $m$ falls from the tree through a vertical distance of $s$ and could reach ground with a velocity of $v$ ms${}^{-1}$ due to air resistance. Work done by air resistance is :

• A. $-\frac{m}{2}(2gs-v^2)$
• B. $-\frac{1}{2}m{v}^2$
• C. $mgs$
• D. $m{v}^2+2mgs$

Answer 1

The correct option is A $-\frac{m}{2}(2gs-v^2)$

Work done $=$ Change in K.E.
i.e. $W_g+W_a=\frac{1}{2}m{v}^2$

where $W_g=mgs$ and $W_a$ is the work done by air resistance

$\therefore =W_a=-mgs+\frac{1}{2}m{v}^2$

$=-\frac{m}{2}(-v^2+2gs)$

$=-\frac{m}{2}(2gs-v^2)$