Gravitational acceleration on the surface of a planet is 6 11 g , where g is the gravitational acceleration on the surface of the Earth. The average mass density of the planet is 2 3 times that of the Earth. If the escape speed on the surface of the earth is taken to be 11 km s - 1 , the escape speed on the surface of the planet in km s - 1 will be:

Suppose density of planet is ρ , mass of planet is M and radius of planet is R . Acceleration due to gravity, g = G M R 2 = G 4 3 π R 3 ρ R 2 or g ∝ ρ R Now escape velocity, v e = 2 g R = 2 g 2 ρ or v e Earth v e Planet = g 6 11 g 2 × ρ Planet ρ Earth Or v e Earth v e Planet = 11 6 × 2 3 v e Earth v e Planet = 11 3 v e Planet = 3 km s - 1 ∴ v e planet = 9 . 8 6 121 × 3 2 = 3 km s - 1

HARD

11th West Bengal Board

IMPORTANT

Earn 100

Two uniform solid spheres of equal radii $R$ , but masses $M$ and $4 M$ have a centre to centre separation of $6 R$ , as shown in Fig. $12.53$ . The two spheres are held fixed. A projectile

of mass $m$ is projected from the surface of the sphere of mass $M$ directly towards the centre of the second sphere. Obtain an expression for the minimum speed $v$ of the projectile so that it reaches the surface of the second sphere.

Important Questions on Gravitation

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 14

A particle of mass

m

is placed at the centre of a uniform spherical shell of equal mass and radius

a

. Find the gravitational potential at a point

- \frac{G M m}{2 R} - \frac{G M m}{R}

at a distance

\frac{a}{2}

from the centre.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 15

In a region in a gravitational field, the gravitational potential at a point

r (x, y)

is given by

V = 30 (x + y) J / kg

. Find the gravitational field at that point and calculate the force on a particle of mass

0.5 kg

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 16

A uniform rod of mass

M

and length

L

is situated along the

x

-axis, with its centre at the origin. Find the gravitational field due to the rod at a distance

x

from its centre along the

x

-axis, where

x > \frac{L}{2}

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 17

Three particles, each of mass

m

, are situated at the vertices of an equilateral triangle of side length

{}^{'}a^{'}

. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original mutual separation

a

. Find the initial velocity that should be given to each particle and also the time period of the circular motion.

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 18

Gravitational acceleration on the surface of a planet is $\frac{\sqrt{6}}{11} g$ , where g is the gravitational acceleration on the surface of the Earth. The average mass density of the planet is $\frac{2}{3}$ times that of the Earth. If the escape speed on the surface of the earth is taken to be $11 km s^{- 1}$ , the escape speed on the surface of the planet in $km s^{- 1}$ will be:

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 19

A binary star consists of two stars

A

(mass

2.2 M_{s}

) and

B

(mass

11 M_{s}

), where

M_{s}

is the mass of the sun. They are separated by a distance

d

and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star

B

about the centre of mass is

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 20

Estimate whether it takes more energy to get a satellite upto

1600 k m

above the earth than to put in orbit there? Does your answer remain same for a height of

3200 k m

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 21

Sun and the earth revolve around a common centre of mass with common period of revolution

T

. If

M_{s}

and

M_{e}

are the masses of the sun and earth respectively and

a

is distance between them, then prove that

M_{s} + M_{e} = \frac{4 π^{2}}{G} \times \frac{a^{3}}{T^{2}}

Important Questions on Gravitation

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