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 , where R is the radius of earth. Reason R : The m

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Solution

Q.
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 $\frac{1}{2} m g R$ , 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 [2025]

1 A is false but R is true

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

3 A is true but R is false

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

Ans.
(1)

At $\infty$ , PE is zero, U = 0

$\frac{1}{2} m v^{2} - \frac{G M m}{R} = 0$

$KE = \frac{G M}{R^{2}} \cdot m R = m g R$

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