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The speed of a comet at perihelion (closest to the sun) is $5.6 \times 10^{4} {ms}^{- 1},$ while its distance from the sun is $9.0 \times 10^{10} m .$ At aphelion (farthest from the sun) its distance is $5.6 \times 10^{12} m .$ The comet's aphelion speed is:

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Important Questions on Gravitation

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 4

Two stars of masses

M_{1}

and

M_{2}

form a binary system. The distance between the centres of the stars is

d .

The orbital period is given by

EASY

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 5

Ocean tides on the Earth are caused by the gravitational effects of the Moon (for lunar tides) as well as the Sun (for solar tides). If the diameter of the earth were to increase by

20 %

then

HARD

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 6

A certain planet completes one rotation about its axis in time

T .

The weight of an object placed at the equator on the planet's surface is a fraction

f

(

f

is close to unity) of its weight recorded at a latitude of

60 ° .

The density of the planet (assumed to be a uniform perfect sphere) is given by:

HARD

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 7

A comet (assumed to be in an elliptical orbit around the sun) is at a distance of

0.4 AU

from the sun at the perihelion. If the time period of the comet is

125

years, what is the aphelion distance?

AU

: astronomical unit.

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 8

A small asteroid is orbiting around the sun in a circular orbit of radius

r_{0}

with speed

V_{0}

. A rocket is launched from the asteroid with speed,

V = α V_{0}

, where

V

is the speed relative to the sun. The highest value of

α

for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effect of other planets),

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 9

A planet orbits in an elliptical path of eccentricity $e$ around a massive star considered fixed at one of the foci. The point in space where it is closest to the star is denoted by $P$ and the point where it is farthest is denoted by $A$ . Let $v_{P}$ and $v_{A}$ be the respective speeds at $P$ and $A$ . Then,

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 10

A body moves in a circular orbit of radius

R

under the action of a central force. The potential due to the central force is given by,

V (r) = k r

(

k

is a positive constant). The period of revolution of the body is proportional to,

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Practice Book for KVPY Aptitude Test - Stream SX Physics>Chapter 2 - Gravitation>Exercise#2>Q 11

If the axis of rotation of the earth were extended into space, then it would pass close to,

The speed of a comet at perihelion (closest to the sun) is 5.6×104 ms-1, while its distance from the sun is 9.0×1010 m. At aphelion (farthest from the sun) its distance is 5.6×1012 m. The comet's aphelion speed is:

Important Questions on Gravitation

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The speed of a comet at perihelion (closest to the sun) is $5.6 \times 10^{4} {ms}^{- 1},$ while its distance from the sun is $9.0 \times 10^{10} m .$ At aphelion (farthest from the sun) its distance is $5.6 \times 10^{12} m .$ The comet's aphelion speed is: