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
B
2GMR
C
GM2R
D
GM4R

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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