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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is (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 option given below

Both A and R are true and R is the correct explanation of A

(4) Both A and R are true but R is NOT the correct explanation of A

Gravitation

JEE Main level, single correct, medium

108 of 223

Question 108 of 223

Given below are two statements: one is labelled as Assertion $\mathrm{A}$ and the other is labelled as Reason $\mathrm{R}$ Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$ , where R is the radius of earth.
Reason $\mathrm{R}$ : 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 option given below

Show answer and solution

Answer: (A) $\mathrm{A}$ False but $\mathrm{R}$ is true

\mathrm{KE}=\frac{1}{2} \mathrm{~m}\left(\frac{2 \mathrm{Gm}}{\mathrm{R}}\right)=\mathrm{mgR}

Assertion wrong
at

\infty

\mathrm{U}=0

\therefore

Reason correct.

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