The gravitational field in a region is given by F = 10 i ^ + 5 k ^ N / Kg . Find the work to be done if a body of mass 0 . 5 kg is taken from the origin to the point 5 m , 0 , 6 m

Given, The gravitational field F = 10 i ^ + 5 k ^ , r = 5 m , 0 , 6 m dV = F . dr = 10 i + 5 k . 5 i + 6 k = 50 + 30 = 80 , ∵ i . ^ i ^ = j . ^ j ^ = k ^ . k ^ = 1 Work to be done by mass m = 0 . 5 Kg , W = m × dV = 0 . 5 × 80 = 40 J .

HARD

11th West Bengal Board

IMPORTANT

Earn 100

The planet Mars has two moons. Phobos and Demos. (i) Phobos has period $7$ hour $39$ minute and an orbital radius of $9.4 \times 10^{3} km$ . Calculate the mass of the Mars. (ii) Assume the earth and the mars move in circular orbits around the sun, with the martian orbit being $1.52$ times the orbital radius of the earth. What is the length of the Martian year in days?

Important Questions on Gravitation

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 33

The gravitational field in a region is given by

F = 10 \hat{i} + 5 \hat{k} N / Kg

. Find the work to be done if a body of mass

0.5 kg

is taken from the origin to the point

(5 m, 0, 6 m)

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 34

A saturn year is

29.5

times the earth year. How far is the saturn from the sun if the earth is

1.50 \times 10^{8} km

away from the sun?

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 1

A uniform sphere has a radius

0.02 m

. Find the percentage of increase in its weight when a second sphere of radius

0.2 m

and density

12 \times 10^{3} kg m^{- 3}

is brought under it almost in contact with it.

G = 6.67 \times 10^{- 11} SI

and

g = 9.8 m s^{- 2}

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 2

The density within the earth of radius

R

is given by

ρ_{x} = ρ R / x

where

ρ

is the density at the surface and

x

denotes the distance of a point within the sphere from the centre of the earth. Find the gravitational field due to the earth at a distance

2 R

from its centre.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 3

Two bodies of mass

m

and

M

are initially at an infinite distance away from each other. Then, they begin to approach each other being attracted by the gravitational force of attraction on each other. When they are at a distance

r

apart, show that the velocity of their approach is

\sqrt{\frac{2 G}{r} (M + m)}

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 4

Calculate the distance from the surface of the earth at which above and below, the accelerations due to gravity is the same.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 5

If the earth were a solid sphere of iron of radius

6.37 \times 10^{6} m

and of density

7.86 gm / cc

what would be the value of the acceleration due to gravity at its surface, taking the gravitational constant to be

6.58 \times 10^{- 8} CGS unit

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 11 - Gravitation>EXERCISE>Q 6

Two masses

m_{1}

and

m_{2}

revolve round a common centre of mass, forming a binary system. Show that the common time-period

T

is given by,

T = 2 π r \sqrt{\frac{r}{G (m_{1} + m_{2})}}

where

r

is the distance between the two masses.

Important Questions on Gravitation

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