If a body of mass 1 kg falls on the earth from infinity, it attains… | JEE Main 2026 (2 Apr, Shift 2)

Q8JEE Main 2026 · 2 APR · SHIFT 2Medium

Escape Velocity

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 m/s2)

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Answer: (a)

Falling from infinity, the body arrives with the escape speed: $v = \sqrt{2gR}$ .
$v = \sqrt{2\times9.8\times6.4\times10^{6}} = \sqrt{1.254\times10^{8}} \approx 11.2\text{ km/s}$ .
$k = \frac{1}{2}mv^2 = \frac{1}{2}\times1\times1.254\times10^{8} = 6.27\times10^{7}$ J.
So the answer is (a) 11.2 km/s; $6.27\times10^{7}$ J.

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