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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Physics
Chapter
Gravitation

BITSAT 2024 · Physics · Gravitation

A body which is initially at rest at a height R above the surface...

A body which is initially at rest at a height RR above the surface of the Earth of radius R, falls freely towards the Earth, then its velocity on reaching the surface of the Earth is

Options

  1. A(2gR)\sqrt{(2 g R)}
  2. B(gR)\sqrt{(g R)}
  3. C32gR\sqrt{\frac{3}{2} g R}
  4. D(4gR)\sqrt{(4 g R)}

Correct answer

B. (gR)\sqrt{(g R)}

Step-by-step solution

Increase in kinetic energy = Decrease in potentialenergypotential energy∴12mv2=mgR1+RR=mgR2(ΔU=mgh1+hR,h=R)⇒mv2=mgR⇒v=gR\begin{aligned} & \therefore \quad \frac{1}{2} m v^2=\frac{m g R}{1+\frac{R}{R}}=\frac{m g R}{2} \quad\left(\Delta U=\frac{m g h}{1+\frac{h}{R}}, h=R\right) \\ & \Rightarrow \quad m v^2=m g R \Rightarrow v=\sqrt{g R} \end{aligned}$$
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