Question

A man can jump to a height 2 m on earth. If density is $1/3rd$ and radius $1/4^{th}$ that of earth, the height, he might be able to jump to is

• A. 32 m
• B. 24 m
• C. 6 m
• D. 12 m

Answer 1

The correct option is B 24 m

$\text{energy will be same}$

$P_m=mgh$

$\text{if density and radius changes}$

$\text{value of g changes.}$

$g=\frac{GM}{R^2}=\frac{Gd\times \frac{4}{3}\pi R^3}{R^2}$

$=\frac{4Gd\pi R}{3}$

Now

$\frac{M\times \text{4Gd}\pi R}{3}\times 2=m\times \frac{4\text{Gd}\pi R}{3\times 3\times 4}\times h$

$h=24m$

Answer: $-\left(B\right)$