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Question

A particle is situated at a height $$3\ R$$ from the earth surface. The velocity with which it should be projected vertically upward so that it does not return to earth is:


A
GMR
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B
2GMR
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C
GM2R
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D
GM4R
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Solution

The correct option is A $$\sqrt {\dfrac {GM}{2R}}$$
Conserving mechanical energy
$${ E }_{ i }={ E }_{ f }$$
$$\dfrac { -GMm }{ 3R+R } +\dfrac { 1 }{ 2 } { mV }^{ 2 }=0+0$$
$$\Rightarrow \quad \dfrac { GM }{ 4R } =\dfrac { 1 }{ 2 } { V }^{ 2 }$$
$$\Rightarrow \quad V=\sqrt { \dfrac { GM }{ 2R }  } $$

Physics

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