Given below are two statements: one is labelled as Assertion A and… | JEE Main 2025 (4 Apr, Shift 1)

Q11JEE Main 2025 · 4 APR · SHIFT 1Easy

Escape Velocity

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A: The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2}mgR$ , where R is the radius of earth.

Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.

In the light of the above statements, choose the correct answer from the options given below

Show answer and solution

Answer: (a)

KE needed $= \frac{GMm}{R} = mgR$ , not $\frac{1}{2}mgR$ , so A is false.
PE $= -\frac{GMm}{r}$ rises to its maximum value zero at infinity, so R is true.
So the answer is (a).

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