Question

A body having a mass of $100\text{gm}$ is allowed to fall freely (from a very large height) under the action of gravity. Work done by gravity during first $10\text{s}$ of journey is (Take $g=10{\text{m/s}}^2$)

• A. $500000\text{J}$
• B. $50000\text{J}$
• C. $5000\text{J}$
• D. $500\text{J}$

Answer 1

The correct option is D $500\text{J}$

Given, mass of a body $=100\text{gm}=0.1\text{kg}$

Since, the body is under free fall, $u=0$
Using, $s=ut+\frac{1}{2}a{t}^2$, we get
$s=\frac{1}{2}g{t}^2$
$\Rightarrow s=\frac{1}{2}\times 10\times (10{)}^2=\frac{1000}{2}=500\text{m}$
Force of gravity $\left(F\right)=mg=0.1\times 10=1\text{N}$
Workdone by gravity $\left(W\right)=\overrightarrow{F}.\overrightarrow{s}=Fs$, as $\cos 0^{\text{o}}=1$
($\because$ force of gravity is along same direction as displacement)
$W=1\times 500=500\text{J}$

Hence option D is the correct answer