Question

A body of mass 100 kg falls on the earth from infinity. What will be its energy on reaching the earth? Radius of the earth is 6400 km and g = 9.8 $m/s^2$. Air friction is negligible.

• A. 6.27 x ${10}^9$ J
• B. 6.27 x ${10}^{10}$ J
• C. 6.27 x ${10}^{12}$ J
• D. 6.27 x ${10}^7$ J

Answer 1

The correct option is A 6.27 x ${10}^9$ J

$\begin{array}{c}u\hat{i}+k\hat{i}=u_f+k_f\\ \Rightarrow 0+0=\frac{-GMm}{R}+\frac{1}{2}m{v}^2\\ \Rightarrow \frac{1}{2}m{v}^2=\frac{GMm}{R\times R}\times R\\ =mgR\\ =100\times 9.8\times 6400\times 1000\\ =6272000\times 1000\\ =6.27\times {10}^{9}J\end{array}$

Hence,

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