The kinetic energy needed to project a body of mass $m$ from the earth surface (radius $R$ ) to infinity is

The kinetic energy needed to project a body of mass $m$ from the earth surface (radius $R$ ) to infinity is
  1. $\mathrm{mgR} / 2$
  2. $2 \mathrm{mgR}$
  3. $\mathrm{mgR}$
  4. $\mathrm{mgR} / 4$

Solution

$\mathrm{KE}=\frac{1}{2} \mathrm{mv}_{\mathrm{esc}}^2=\frac{1}{2} \mathrm{~m}(\sqrt{2 \mathrm{gR}})^2=\mathrm{mgR}$

Asked in: JEE Main 2002

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