Two satellites of earth, S 1 and S 2 , are moving in the same orbit. The mass of S 1 is four times the mass of S 2 . Which one of the following statements is true?

S 1 and S 2 are moving at the same speed.

The time period of S 1 is four times that of S 2 .

The potential energies of the earth and satellite in the two cases are equal.

The kinetic energies of the two satellites are equal.

Physics - Gravitation - Quiz-8

A body of mass ‘m’ is taken from the Earth’s surface to the height equal to twice the radius (R) of the Earth. The change in potential energy of the body will be:

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2/3mgR
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3mgR
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1/3mgR
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2mgR

An infinite number of bodies, each of mass 2 kg are situated on the x-axis at distances 1m, 2m, 4m, 8m, ........ respectively, from the origin. The resulting gravitational potential due to this system at the origin will be :

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$- \frac{8}{3} G$
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$- \frac{4}{3} G$
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–4G
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–G

A spherical planet has a mass $M_{p}$ and diameter $D_{p}$ . A particle of mass m falling freely near the surface of this planet will experience acceleration due to gravity equal to:

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$\frac{4 {GM}_{p} m}{{D_{p}}^{2}}$
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$\frac{4 {GM}_{p}}{{D_{p}}^{2}}$
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$\frac{{GM}_{p} m}{{D_{p}}^{2}}$
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$\frac{{GM}_{p}}{{D_{p}}^{2}}$

The figure shows the elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t₁ is the time for the planet to move from C to D and t₂ is the time to move from A to B, then,

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t₁> t₂
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t₁ = 4t₂
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t₁ = 2t₂
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t₁ = t₂

Two satellites of earth, S₁ and S₂, are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which one of the following statements is true?

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S₁ and S₂are moving at the same speed.
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The time period of S₁ is four times that of S₂.
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The potential energies of the earth and satellite in the two cases are equal.
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The kinetic energies of the two satellites are equal.

The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fv_e, where v_e is its escape velocity from the surface of the earth. The value of f is :

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$\sqrt{2}$
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$\frac{1}{\sqrt{2}}$
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$\frac{1}{3}$
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$\frac{1}{2}$

The gravitational field due to a mass distribution is given by $\vec{I} = \frac{k}{x^{2}} \hat{i}$ , where k is a constant. Assuming the potential to be zero at infinity, find the potential at a point x = a.[This question includes concepts from Gravitation chapter]

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$\frac{k}{a^{2}}$
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$\frac{- k}{a^{2}}$
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$\frac{k}{a}$
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$\frac{- k}{a}$

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is:

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$\frac{3}{2} m g R$
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mgR
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2mgR
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$\frac{1}{2} m g R$

A body weighs 200 N on the surface of the earth. How much will it weigh halfway down the centre of the earth?

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100 N
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150 N
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200 N
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250 N

A planet whose density is double of earth and radius
is half of the earth, will produce gravitational field on its
surface (g = acceleration due to gravity at the surface of
earth):

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g
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2g
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$\frac{g}{2}$
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3g

Which of the following graphs represents correctly the variation of intensity of gravitational field l with the distance r from the centre of a spherical shell of mass M and radius a?

A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre-

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Increases
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Decreases
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Remains constant
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Oscillates

A mass falls from a height 'h' and its time of fall 't' is recorded in terms of time period T of a simple pendulum. On the surface of the earth, it is found that t=2T. The entire set up is taken on the surface of another planet whose mass is half of that of the earth and radius is same. The same experiment is repeated and corresponding times noted as t' and T'. Then we can say:

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t' = $\sqrt{2} T$
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t' > 2T'
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t' < 2T'
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t' = 2T'

The time period of a geostationary satellite is 24 h at a height 6 $R_{E}$ ( $R_{E}$ is the radius of the earth) from the surface of the earth. The time period of another satellite whose height is 2.5 $R_{E}$ from the surface, will be:

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6 $\sqrt{2} h$
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12 $\sqrt{2} h$
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$\frac{24}{2.5} h$
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$\frac{12}{2.5} h$

Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final - initial) of an object of mass m when taken to a height h from the surface of the earth (of radius R and mass M), is given by:

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$\frac{G M m}{R + h}$
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$\frac{G M m h}{R (R + h)}$
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mgh
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$\frac{G M m}{R + h}$

A particle of mass M is at distance 'a' from the surface of a thin spherical shell of mass M and radius
a. If $V_{o} and V_{s}$ are the potentials at the centre and the surface of the shell respectively, then

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$V_{S} > V_{O}$
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$V_{S} < V_{O}$
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$V_{S} = V_{O}$
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Can't say

The distance between the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth the gravitational force will be zero ?

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$\frac{D}{2}$
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$\frac{2 D}{2}$
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$\frac{4 D}{3}$
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$\frac{9 D}{10}$

Which one of the following plots represent

the variation of gravitational field on a

particle at distance r, due to a thin

spherical shell of radius R? (r is measured

from the centre of the spherical shell).

Two concentric shells of uniform density of mass M and 2M are situated as shown in the figure. The ratio of forces experienced by a particle of mass m at position A and B is:

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2:1
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1:2
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4:3
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3:2

A tunnel has been dug through a diameter of a solid sphere of uniform mass density. Which graph best represents the variation of gravitational field intensity E with position r as one moves from A to B?

Assuming the earth as a uniform solid sphere of radius R, the gravitational field on its surface is x. The gravitational field inside at a distance $\frac{R}{2}$ from its surface is

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x
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$\frac{x}{3}$
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2x
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$\frac{x}{2}$

Variation of gravitational field due to a uniform solid sphere of radius R with distance r from the centre is

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Straight line, for R < r
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Hyperbolic, for R > r
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Parabolic for R < r
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Both (1) & (2)

In the following questions, a statement of assertion (A) is followed by a statement of the reason (R)

A: The gravitational field due to earth is zero both at the center of the earth and at infinite distance.

R: The gravitational potential of the earth is zero at the center of the earth and at infinity

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If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
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If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
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If Assertion is a true statement but Reason is false, then mark (3)
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If both Assertion and Reason are false statements, then mark (4)

A body weighs 72 N on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth?

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32 N
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30 N
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24 N
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48 N

What is the depth at which the value of acceleration due to gravity becomes 1/n times the value of that at the surface of the earth? (radius of earth = R)

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R/ $n^{2}$
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R(n – 1)/n
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Rn/(n – 1)
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R/n

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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