Q 11-07-044JEE MainJEE Main 2026 (2 Apr, Shift 2)Easy
If a body of mass $1$ kg falls on the earth from infinity, it attains velocity $(v)$ and kinetic energy $(k)$ on reaching the surface of earth. The values of $v$ and $k$ respectively are ______.
(Take radius of earth to be $6400$ km and $g=9.8\ \text{m/s}^2$)
Answer: (A) $11.2$ km/s; $6.27\times10^{7}$ J
Energy conservation from infinity (energy $0$) to the surface: $\tfrac12mv^2-\dfrac{GMm}{R}=0$, so $v=\sqrt{\dfrac{2GM}{R}}=\sqrt{2gR}$ (the escape speed).
$v=\sqrt{2\times9.8\times6.4\times10^{6}}=\sqrt{1.2544\times10^{8}}=1.12\times10^{4}$ m/s $=11.2$ km/s
$k=\tfrac12mv^2=\tfrac12\times1\times1.2544\times10^{8}=6.27\times10^{7}$ J
Solution by Sreeraj P, M.Sc Physics