Question

A rocket is launched with velocity of $10km{s}^{-1}$. If radius of earth is $R$ then maximum height attained by it will be:

• A. $2R$
• B. $3R$
• C. $4R$
• D. $5R$

Answer 1

The correct option is C $4R$

Given,

$v=10km/s$

$R=$ radius of the earth

When a rocket is launched, kinetic energy is converted into potential energy.

At maximum height, potential energy is equal to the kinetic energy.

$P.E=K.E$

$mg(R+H)=\frac{m{v}^2}{2}$

$R+H=\frac{v^2}{2g}$

$R+H=\frac{10\times 1000\times 10\times 1000}{2\times 10}$

$R+H=5R$ (as $R=6.5\times {10}^{6}m$)

$H=4R$

The correct option is C.