A space-ship is stationed on the planet venus. How much energy must be expanded on the space-ship to rocket it out of the solar system? Given that mass of the space-ship m = 800 kg , mass of the sun M = 2 × 10 30 kg ; mass of the venus M V = 5 . 0 × 10 24 kg , radius of the venus R V = 6 , 000 km , radius of the orbit of the venus r = 1 . 00 × 10 11 m and gravitational constant, G = 6 . 6 × 10 - 11 N m 2 kg - 2 .

The PE of the spaceship-Venus system, U 1 = - G M V m R V = - 6 . 6 × 10 - 11 × 5 . 0 × 10 24 × 800 6 . 0 × 10 6 = - 4 . 4 × 10 10 J And PE of the spaceship-sun system, U 2 = - G M s m r = - 6 . 6 × 10 - 11 × 2 × 10 30 × 800 1 . 0 × 10 11 = - 1 . 05 × 10 12 J Therefore, total potential energy of the spaceship, U = U I + U 2 = - 4 . 4 × 10 10 + - 1 . 05 × 10 12 = - 1 . 1 × 10 12 J Hence, energy required to rocket the spaceship out of the solar system = 0 - U = 0 - - 1 . 1 × 10 12 = 1 . 1 × 10 12 J

HARD

JEE Advanced

IMPORTANT

Earn 100

Does a planet revolving around the sun in elliptical orbit have a constant _____ throughout its orbit?

(a) linear speed

(b) angular momentum

(c) kinetic energy

(d) potential energy

Important Questions on Gravitation

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 2

Three mass points each of mass

m

are placed at the vertices of an equilateral triangle of side

l .

What is the gravitational field and potential due to three masses at the centroid of the triangle?

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 3

g

is the acceleration due to gravity on the earth's surface, what will be the gain in the potential energy of an object of mass

m

raised from the surface of the earth to a height equal to twice the radius of the earth?

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 4

Find the potential energy of the system of three particles.

Question Image

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 5

Find the minimum energy required to disassemble the system of three particles.

Question Image

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 6

With what velocity should an object be projected from the surface of the earth, so that its height above the surface becomes equal to the radius of the earth?

MEDIUM

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 7

The masses and radii of the earth and moon are

M_{1}, R_{1}

and

M_{2}, R_{2}

respectively. Their centres are at a distance

r

apart. Find the minimum speed with which a body of mass

m

should be projected from a point mid-way between the centres of the earth and moon so as to escape their gravitational pull.

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 8

Two masses

M_{1}

and

M_{2}

are initially at rest at infinite distance apart. They approach each other due to gravitational interaction. Find their speed of approach at the instant, when they are distance

r

apart.

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 9

A space-ship is stationed on the planet venus. How much energy must be expanded on the space-ship to rocket it out of the solar system? Given that mass of the space-ship

m = 800 kg,

mass of the sun

M = 2 \times 10^{30} kg;

mass of the venus

M_{V} = 5.0 \times 10^{24} kg,

radius of the venus

R_{V} = 6, 000 km,

radius of the orbit of the venus

r = 1.00 \times 10^{11} m

and gravitational constant,

G = 6.6 \times 10^{- 11} N m^{2} {kg}^{- 2} .

Does a planet revolving around the sun in elliptical orbit have a constant _____ throughout its orbit? (a) linear speed (b) angular momentum (c) kinetic energy (d) potential energy

Important Questions on Gravitation

Learn and Prepare for any exam you want !

Does a planet revolving around the sun in elliptical orbit have a constant _____ throughout its orbit?

(a) linear speed

(b) angular momentum

(c) kinetic energy

(d) potential energy