ExamBro
ExamBro
AP EAMCET · PHYSICS · Gravitation

A body is projected vertically from the surface of the earth of radius \(R\) with a velocity equal to half of the escape velocity. The maximum height reached by the body is

  1. A \(\frac{R}{2}\)
  2. B \(\frac{R}{3}\)
  3. C \(\frac{R}{4}\)
  4. D \(\frac{R}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{R}{3}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { } K_f+P_f=K_i+P_i \\ & \mathrm{O}-\frac{G M m}{R+h}=\frac{1}{2} m\left(\frac{V_e}{2}\right)^2-\frac{G M m}{R} \\ & -\frac{G M m}{1}\left[-\frac{1}{R}+\frac{1}{R+h}\right]=\frac{1}{8} m V_e^2\end{aligned}\)…