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NEET 2006
Exam
NEET
Year
2006
Subject
Physics
Chapter
Gravitation

NEET 2006 · Physics · Gravitation

The Earth is assumed to be a sphere of radius R . A platform is...

The Earth is assumed to be a sphere of radius RR. A platform is arranged at a height RR from the surface of the Earth. The escape velocity of a body from this platform is fvf v, where vv is its escape velocity from the surface of the Earth. The value of ff is:

Options

  1. A12\frac{1}{2}
  2. B2\sqrt{2}
  3. C12\frac{1}{\sqrt{2}}
  4. D13\frac{1}{3}

Correct answer

C. 12\frac{1}{\sqrt{2}}

Step-by-step solution

We know that Escape velocity Ve=2gRV_e=\sqrt{2 g R} Escape velocity of the body from platform P. E+K⋅E=0−GMm2R+12mV2=0⇒V=GMR2⋅R=gR\begin{aligned} & \text{P. } \mathrm{E}+\mathrm{K} \cdot \mathrm{E}=0 \\ & -\frac{G M m}{2 \mathrm{R}}+\frac{1}{2} m V^2=0 \\ & \Rightarrow \quad V=\sqrt{\frac{G M}{R^2} \cdot R}=\sqrt{g R} \end{aligned} This confirms that: fv=V2∴f=12.\begin{aligned} & fv =\frac{V}{\sqrt{2}} \\ \therefore f & =\frac{1}{\sqrt{2}} . \end{aligned}
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