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Q.

The minimum KE required to project a body of mass ‘m’ from the earth’s surface to infinity is

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a

mgR

b

mgR/2

c

2mgR

d

mgR/4

answer is C.

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Detailed Solution

When projected with minimum kinetic energy, the body will stop at infinity where potential energy is zero.
Conserving energy $\large (K.E)_{min}+P.E=0$
$\large \Rightarrow (K.E)_{min}+\left ( -\frac {GMm}{R} \right )=0$
$\large \Rightarrow (K.E)_{min}=m.\frac {GM}{R^2}.R=mgR$

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The minimum KE required to project a body of mass ‘m’ from the earth’s surface to infinity is