JEE Main 2026 · 2 Apr · Shift 2 · Physics Q31

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PhysicsSingle correct+4 / -1Question 31 of 75

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)

11.2 km/s;

6.27\times10^7

11.2 km/s;

12.54\times10^7

8.8 km/s;

6.27\times10^7

8.8 km/s;

12.54\times10^7

Answer and worked solution

Official answer: A

Energy from infinity. $\frac12mv^2=\dfrac{GMm}R=mgR$ .

$v=\sqrt{2gR}=\sqrt{2(9.8)(6.4\times10^6)}=11.2$ km/s.
$k=mgR=9.8\times6.4\times10^6=6.27\times10^7$ J.

(A)

Topics:Escape velocity Gravitational field and potential

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JEE Main 2026 · 2 Apr · Shift 2, Physics question 31