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

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.

Important Questions on Gravitation

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} .

EASY

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>CONCEPT APPLICATION EXERCISE>Q 1

Air friction increases the velocity of the satellite. Explain.

EASY

JEE Advanced

IMPORTANT

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

Two satellites move along a circular orbit in the same direction at a small distance from each other. A container has to be thrown from the first satellite on the second one. When will the container reach the second satellite earlier, if it is thrown in the direction of motion of the first satellite or in the opposite direction? The velocity of the container is small in comparison to that of the satellite.

EASY

JEE Advanced

IMPORTANT

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

Two satellites of the same mass are launched in the same orbit around the earth so as to rotate opposite to each other. They collide inelastically and stick together as wreckage. Obtain the total energy of the system before and just after the collision. Describe the subsequent motion of the wreckage.

EASY

JEE Advanced

IMPORTANT

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

If a satellite is revolving around a planet of mass $M$ in an elliptical orbit of semi-major axis

a .

Show that the orbital speed of the satellite when it is at a distance

r

from the planet will be given by

v^{2} = G M [\frac{2}{r} - \frac{1}{a}] .

MEDIUM

JEE Advanced

IMPORTANT

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

An artificial satellite is in a circular orbit at $500 km$ above the earth's surface.

(i) What is the acceleration of the satellite?

(ii) What is the acceleration due to gravity at any point along the satellite's path?

Take radius of the earth as $6.5 \times 10^{6} m .$

EASY

JEE Advanced

IMPORTANT

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

A satellite of mass

m

moves in a circular orbit of radius

r

around the earth. Calculate the total energy required to place the satellite in the orbit from the earth's surface. Assuming initially it to be at rest.

EASY

JEE Advanced

IMPORTANT

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

A satellite is lifted from earth to a height $h .$ Let the work done by the external agent be $W_{1} .$ Then it is projected with a speed $v$ so as to move in a circular orbit doing an extra work $W_{2} .$ Compare these works done.

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Two masses M1 and M2 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.

Important Questions on Gravitation

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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.