Question

How much energy will be needed for a body of mass 100$kg$ to escape from the earth$(g=10m/s^2)$ and radius of earth $=6.4\times {10}^{8}m$

• A. $6.3\times {10}^9$ joule
• B. $8\times {10}^6$ joule
• C. $4\times {10}^6$ joule
• D. zero

Answer 1

The correct option is A $6.3\times {10}^9$ joule

Energy balance

$K{E}_i+P{E}_i=K{E}_f+P{E}_f$

$\Rightarrow \frac{1}{2}m{v}^2-\frac{GMm}{R}=0-0$

$\Rightarrow \frac{1}{2}m{v}^2=\frac{GMm}{R}$

$v=\sqrt{\frac{2GM}{R}}=\sqrt{2gR}$

$v=11.2km/c$

$Energygiven=\frac{1}{2}m{v}^2=\frac{1}{2}\times 100\times {\left(11.2\times {10}^3\right)}^2$

$\Rightarrow 6.3\times {10}^{9}J$

Hence,

option $\left(A\right)$ is correct answer.