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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationEnergy & PotentialEasy2 minPYQ_2020

PhysicsEasysingle choice

A particle is projected vertically with speed $V$ from the surface of the earth. Maximum height attained by the particle, in terms of the radius of earth $R, V$ and $g$ is ( $V <$ escape velocity, $g$ is the acceleration due to gravity on the surface of the earth)

Options:

Answer:

Solution:

$\frac{1}{2} m V^{2} - \frac{G M m}{R} = \frac{- G M m}{R + h}$

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

$\frac{1}{2} V^{2} - g R = \frac{- g R^{2}}{(R + h)}$

$R + h = \frac{- 2 g R^{2}}{V^{2} - 2 g R}$

$h = \frac{- 2 g R^{2}}{V^{2} - 2 g R} - R$

$h = \frac{- R V^{2}}{V^{2} - 2 g R}$

$h = \frac{R V^{2}}{2 g R - V^{2}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:GravitationSubtopic:Energy & Potential

⏱ 2mℹ️ Source: PYQ_2020

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