Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationEnergy & PotentialEasy2 minPYQ_2020

PhysicsEasysingle choice

A body is thrown from the surface of the earth with velocity $u m s^{- 1}$ . The maximum height in meter above the surface of the earth up to which it will reach is ( $R =$ radius of the earth, $g =$ acceleration due to gravity)

Options:

Answer:

Solution:

$\frac{- G M m}{R} + \frac{1}{2} m u^{2} = 0 + (- \frac{G M m}{R + h})$

$\frac{G M}{R + h} = \frac{G M}{R} - \frac{u^{2}}{2}$

$\frac{G M}{(R + h)} = \frac{2 GM - R u^{2}}{2 R}$

$\frac{R + h}{G M} = \frac{2 R}{2 G M - R u^{2}}$

$h = \frac{2 G M R}{2 G M - R u^{2}} - R$

$= \frac{2 G M R - 2 G M R + R^{2} u^{2}}{2 G M - R u^{2}}$

$= \frac{R^{2} u^{2}}{2 G M - R u^{2}} = \frac{R u^{2}}{2 g R - u^{2}}$

Subject:PhysicsTopic:GravitationSubtopic:Energy & Potential

⏱ 2mℹ️ Source: PYQ_2020

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