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Gravitation MCQs for NEET — Physics Questions with Answers

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What will be the acceleration due to gravity at height h if h >> R where R is radius of earth and g is acceleration due to gravity on the surface of earth ?

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

$g (1 - \frac{2 h}{R})$

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

$g (1 - \frac{h}{R})$

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Explanation

(a) g'=g ${(\frac{R}{R + h})}^{2} = \frac{g}{{(1 + \frac{h}{R})}^{2}}$

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How many times is escape velocity, of orbital velocity for a satellite revolving near earth?

$\sqrt{2}$ times

2 times

3 times

4 times

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Explanation

(a)

$E s c a p e v e l o c i t y = \sqrt{\frac{2 G M}{R}} O r b i t a l v e l o c i t y = \sqrt{\frac{G M}{R}} H e n c e, i t' s \sqrt{2} t i m e s .$

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Escape velocity on earth is 11.2 km/s. What would be the escape velocity on a planet whose mass is 1000 times and radius is 10 times that of earth ?

112 km/s

11.2 km/s

1.12 km/s

3.7 km/s

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Explanation

(a) $\frac{v_{p}}{v_{e}} = \sqrt{\frac{M_{p}}{M_{e}} \frac{R_{e}}{R_{p}}} = \sqrt{(1000) \times (\frac{1}{10})} = 10 v_{p} = 10 \times 11.2 = 112 k m / s$

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If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect ?

Viscous forces

Archimedes uplift

Electrostatic force

None of the above

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Explanation

(b) As it depends on the weight of the body.

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The acceleration due to gravity near the surface of a planet of radius R and density d is proportional to

$\frac{d}{R^{2}}$

$d R^{2}$

$\frac{d}{r}$

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Explanation

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The weight of a body at the centre of the earth is -

Zero

Infinite

Same as on the surface of the earth

None of the above

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Explanation

(a)

$F = \frac{G M r}{R^{3}} H e r e, r = 0 s o, F = 0$

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A spherical planet far out in space has a mass $M_{0}$ and diameter $D_{0}$ . A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

$G M_{0} / {D_{0}}^{2}$

$4 m G M_{0} / {D_{0}}^{2}$

$4 G M_{0} / {D^{2}}_{0}_{}$

$G m M_{0} / {D^{2}}_{0}$

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Explanation

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If the radius of a planet is R and its density is $ρ$ , the escape velocity from its surface will be

$V_{e} \propto p R$

$V_{e} \propto R \sqrt{ρ}$

$V_{e} \propto \frac{\sqrt{p}}{R}$

$V_{e} \propto \frac{1}{\sqrt{p} R}$

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Explanation

(b) $v_{e} = R \sqrt{\frac{8}{3} G πρ} s o, v_{e} \propto R \sqrt{ρ}$

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If the distance between two masses is doubled, the gravitational attraction between them

Is doubled

Becomes four times

Is reduced to half

Is reduced to a quarter

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Explanation

(d) $F \propto \frac{1}{r^{2}}$ .

If r becomes double , then F reduces to $\frac{F}{4}$

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If the earth stops rotating, the value of ‘g’ at the equator will

Increase

Remain same

Decrease

None of the above

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Explanation

(a) g increases due to absence of the centrifugal force.

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