Question

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

Answer: (A)

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

Here, a coconut of mass $m$ falls from its tree through a vertical distance of $s$, with a velocity of $v$ hence work done by gravity is,

$W_g=mgs$ .......(1)

Change in velocity of coconut is,

$E=\frac{1}{2}m(u-v{)}^2=-\frac{1}{2}m(v{)}^2$ ........(2)

Now, total work done on coconut is equal to change in kinetic energy hence,

$W_a+W_g=\frac{1}{2}m{v}^2$

where, $W_a$ is work done by air resistance.

Using (1) and (2), we get

$W_a=\frac{1}{2}m{v}^2-W_g$

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

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