Verified Solution • 2025–26 Session moderate

QNEET-2013-Ph-1576: NEET 2013 Physics - Class 11 NEET-2013-Ph-1576 Solution: A particle of mass 'm' is kept at rest at a height 3R from the…

A particle of mass 'm' is kept at rest at a height 3R from the surface of earth where 'R' is radius of earth and 'M' is mass of earth. The minimum speed with which it should be projected so that it does not return back is (g is acceleration due to gravity on the surface of earth)

(\frac{GM}{2R})^{1/2}

(\frac{gR}{4})^{1/2}

(\frac{2g}{R})^{1/2}

(\frac{GM}{R})^{1/2}

Multiple Choice Options

A ${\left( {{{GM} \over {2R}}} \right)^{1/2}}$ ( 2 R GM _ ) 1/2
B ${\left( {{{gR} \over 4}} \right)^{1/2}}$ ( 4 g R _ ) 1/2
C ${\left( {{{2g} \over R}} \right)^{1/2}}$ ( R 2 g _ ) 1/2
D ${\left( {{{GM} \over R}} \right)^{1/2}}$ ( R GM _ ) 1/2

Step-by-Step Verified Solution

The minimum speed with which the particle should be projected from the surface of the earth so that it does not return back is known as escape speed and it is given by v e = 2 G M ( R + h ) Here, h = 3R _ v e = 2 G M ( R + 3 R ) = 2 G M 4 R = G M 2 R = g R 2 ( _ g = G M R 2 )

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