Question

A body of mass 1kg is dropped from a height of 10 m. If it hits the ground with speed 10 m/s, then the work done by air resistance is equal to

• A. $-48J$
• B. $+48J$
• C. $+60J$
• D. $-50J$

Answer 1

The correct option is A $-48J$

Mass of block, $m=1$kg

Height, $H=10$m

Velocity of ground, $V=10$m/s

Initially block released from height H(initial velocity, $u=0$)

We have work done by friction as well as gravity.

Apply work$-$Energy theorem:-

Work done by all the forces$=$change in kinetic energy

$\Rightarrow$ Work done by gravity$+$work done by air resistance$=$Final KE$-$Initial KE

$\Rightarrow mgH+W_f=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

$\Rightarrow 1\times 9.8\times 10+W_f=\frac{1}{2}\times 1\times (10{)}^2-\frac{1}{2}\times 1\times 0$

$\Rightarrow 98+W_f=\frac{100}{2}-0=50$

$\Rightarrow W_f=50-98=-48J$

Work done by friction or air resistance$=W_f=-48J$.