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  • The initial velocity  required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of th

The initial velocity \mathrm{v_i} required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity \mathrm{v}_{e} such that \mathrm{v_i}=\sqrt{\frac{x}{y}}\times \mathrm{v}_{e}. The value of x will be ________.
 
Option: 1 10
Option: 2 20
Option: 3 30
Option: 4 40

Answers (1)

best_answer

Here R = radius of the earth

From energy conservation (For point A and point B)

\begin{array}{l} (T.E)_B=(T.E)_A \\ (P.E)_B+(K.E)_B= (P.E)_A+(K.E)_A \\ \\ \frac{-\mathrm{GMm}}{11 \mathrm{R}}+0=\frac{-\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv_i}^{2} \\ \mathrm{v_i}=\sqrt{\frac{20 \mathrm{GM}}{11 \mathrm{R}}} \end{array}

As

\mathrm{v_e}=\sqrt{\frac{ \mathrm{GM}}{ \mathrm{R}}}

So  \mathrm{v_i}=\sqrt{\frac{ 20}{11}}\mathrm{v_e}

So x=20

Posted by

Deependra Verma

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