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Standard XII

Physics

Gravitational Potential

If the gravit...

Question

If the gravitational potential on the surface of earth is $V_{0}$ then potential at a point at height half of the radius of earth is

\frac{V_{0}}{2}

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\frac{2}{3} V_{0}

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\frac{V_{0}}{3}

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\frac{3 V_{0}}{2}

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Solution

The correct option is B $\frac{2}{3} V_{0}$
$u_{r} = \frac{- G M m}{r} (G r a v i t a t i o n a l p o t e n t i a l)$
$= v_{0}$ at surface
at height $h \sim \frac{r}{2}$
$u_{r^{2}} \sim \frac{- G M m}{\frac{3 r}{2}} = \frac{2}{3} V_{0}$
Hence,
option $(B)$ is correct answer.

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If the gravitational potential on the surface of earth is V0 then potential at a point at height half of the radius of earth is

The correct option is B 23V0ur=−GMmr(Gravitationalpotential)=v0 at surfaceat height h∼r2ur2∼−GMm3r2=23V0Hence,option (B) is correct answer.

If the gravitational potential on the surface of earth is $V_{0}$ then potential at a point at height half of the radius of earth is

The correct option is B $\frac{2}{3} V_{0}$
$u_{r} = \frac{- G M m}{r} (G r a v i t a t i o n a l p o t e n t i a l)$
$= v_{0}$ at surface
at height $h \sim \frac{r}{2}$
$u_{r^{2}} \sim \frac{- G M m}{\frac{3 r}{2}} = \frac{2}{3} V_{0}$
Hence,
option $(B)$ is correct answer.