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A body (mass $m$ ) starts its motion from rest from a point distant $R_0\left(R_0>R\right)$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be ( $G=$ universal constant of gravitation, $M=$ mass of earth. $R=$ radius of earth)

• A
  $2 G M\left(\frac{1}{R}-\frac{1}{R_0}\right)$
• ✓
  $\left[2 G M\left(\frac{1}{R}-\frac{1}{R_0}\right)\right]^{\frac{1}{2}}$
• C
  $G M\left(\frac{1}{R}-\frac{1}{R_0}\right)$
• D
  (b) By using conservation of energy
  Loss in PE Gain in KE
  $$\frac{-GMm}{R_0}-\left(-\frac{GMm}{R}\right)=\frac{1}{2}m{v}^2;v=\sqrt{2GM\left(\frac{1}{R}-\frac{1}{R_0}\right)}$$