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Gravitation

Multiple Choice Questions

21.

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R around the sun will be proportional to

$straight R to the power of open parentheses fraction numerator straight n plus 1 over denominator 2 end fraction close parentheses end exponent$
$straight R to the power of open parentheses fraction numerator straight n minus 1 over denominator 2 end fraction close parentheses end exponent$
Rⁿ
Rⁿ

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22.

A comet orbits around the Sun in an elliptical orbit. Which of the following quantities remains constant during the course of its motion ?

Linear velocity
Angular velocity
Angular momentum
Kinetic energy

23.

Consider a satellite moving in a circular orbit around Earth. If K and V denote its kinetic energy and potential energy respectively, then (Choose the convention, where V = 0 as r → ∞)

K = V
K = 2V
V = − 2K
K = − 2V

24.

Assuming the mass of Earth to be ten times the mass of Mars, its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth is 10 m/s². Then the acceleration due to gravity on the surface of Mars is given by

0.2 m/s²
0.4 m/s²
2 m/s²
4 m/s²

25.

The semi-major axis of the orbit of Saturn is approximately nine times that of Earth. The time period of revolution of Saturn is approximately equal to

81 years
27 years
729 years
$\sqrt[3]{81} years$

26.
A body hanging from a massless spring stretches it by 3 cm on Earth's surface. At a place 800 km above the Earth's surface, the same body will stretch the spring by (Radius of Earth = 6400 km)

$(\frac{34}{27}) cm$

$(\frac{64}{27}) cm$

$(\frac{27}{64}) cm$

$(\frac{27}{34}) cm$

$(\frac{64}{27}) cm$

Acceleration due to gravity,

$g = \frac{GM}{r^{2}} ∴ g \propto \frac{1}{r^{2}}$

When the body is hanged on a spring

F = − kx = mg ..... (i)

acts on it, where x is extension in spring. Let 800 km above the Earth's surface, the stretch in the length of spring is x' and value of g is g'.

$g = \frac{GM}{R^{2}} and g' = \frac{GM}{(R + h)^{2}} So, g' = \frac{g}{{(1 + \frac{h}{R})}^{2}} . . . . . . (ii)$

where, R = radius of Earth

From Eqs.(i), we get

kx = mg ⇒ x ∝ g ...... (iii)

Therefore, $\frac{x'}{x} = \frac{g'}{g}$

From Eqs. (ii) and (iii), we get

$\frac{x'}{x} = \frac{g}{{(1 + \frac{h}{R})}^{2}} / g = \frac{g}{g {(1 + \frac{800 \times 10^{3}}{6400 \times 10^{3}})}^{2}} = \frac{g}{g {(1 + \frac{1}{8})}^{2}} = \frac{g}{g {(\frac{9}{8})}^{2}} = \frac{g \times 64}{g \times 81} = \frac{64}{81} x' = \frac{64}{81} x [x = 3 cm] \Rightarrow x' = \frac{64}{81} \times 3 = \frac{64}{27} \Rightarrow x' = \frac{64}{27} cm$

27.

The acceleration due to gravity on the surface of a planet is one-fourth of the value on Earth. When a brass ball is brought to this planet, its

mass is halved
weight is halved
mass becomes one-fourth
weight becomes one-fourth

28.

Polar satellites

are high altitude satellite
are widely used for telecommunication
are used for environmental studies
go around the Earth in a East-West direction

29.

Angular momentum of the Earth revolving around the Sun in a circular orbit of radius R is proportional to

$\sqrt{R}$
R
R²
R^1/3

30.

A body of mass m is released from a height equal to the radius R of the Earth. The velocity with which it will strike the Earth's surface is

$\sqrt{2 gR}$
$\sqrt{gR}$
$\sqrt{2 mgR}$
$\sqrt{mgR}$

Previous Year Papers

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Multiple Choice Questions

26. A body hanging from a massless spring stretches it by 3 cm on Earth's surface. At a place 800 km above the Earth's surface, the same body will stretch the spring by (Radius of Earth = 6400 km) 3427 cm 6427 cm 2764 cm 2734 cm

26.
A body hanging from a massless spring stretches it by 3 cm on Earth's surface. At a place 800 km above the Earth's surface, the same body will stretch the spring by (Radius of Earth = 6400 km)

$(\frac{34}{27}) cm$

$(\frac{64}{27}) cm$

$(\frac{27}{64}) cm$

$(\frac{27}{34}) cm$