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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationEnergy & PotentialMedium2 minPYQ_2019

PhysicsMediumsingle choice

A body is projected vertically from the surface of the earth of radius ‘ $R$ ’ with velocity equal to half of the escape velocity. The maximum height reached by the body is

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Solution:

From mechanical energy conservation
$k_{i} + U_{i} = k_{f} + U_{f}$
$\Rightarrow \frac{1}{2} m . \frac{2 G M}{4 R} - \frac{G M m}{R} = 0 - \frac{G M m}{r} (∵ v_{e} = \sqrt{\frac{2 G M}{R}})$
$\Rightarrow - \frac{3}{4} . \frac{G M m}{R} = - \frac{G M m}{r}$
$\Rightarrow r = \frac{4 r}{3} \Rightarrow R + h = \frac{4 R}{3} (h = \frac{R}{3})$

Stream:MHT_CETSubject:PhysicsTopic:GravitationSubtopic:Energy & Potential

⏱ 2mℹ️ Source: PYQ_2019

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