A satellite orbits the earth at a height of 500 km from its surface. Calculate total energy. Mass of the satellite is 300 kg , mass of the earth is 6 × 10 24 kg , radius of the earth is 6 . 4 × 10 6 m and G is 6 . 67 × 10 - 11 Nm 2 kg - 2 . Will your answer alter if the earth were to shrink suddenly to half its size ?

Given, Mass of earth, M = 6 × 10 24 kg , Height of satellite from earth surface, h = 500 km = 500 × 10 3 m , Mass of satellite, m = 300 kg Radius of earth, R = 6 . 4 × 10 6 m , Gravitational constant, G = 6 . 67 × 10 - 11 Nm - 2 kg - 2 Kinetic energy of satellite, K . E = 1 2 m v 2 , where v is velocity of satellite v = G M R + h . ∴ K . E . = 1 2 m . G M R + h = 1 2 × 300 × 6 . 67 × 10 - 11 × 6 × 10 24 6 . 4 × 10 6 + 500 × 10 3 = 120 . 06 × 10 7 2 × 6 . 9 = 8 . 7 × 10 9 J Potential energy of satellite P . E = - G M R + h = - 6 . 67 × 10 - 11 × 6 × 10 24 6 . 4 × 10 6 + 0 . 5 × 10 6 = - 6 . 67 × 10 - 11 × 6 × 10 24 × 300 6 . 4 × 10 6 + 0 . 5 × 10 6 = - 17 . 4 × 10 9 J . Total energy = P . E + K . E = 8 . 7 × 10 9 - 17 . 4 × 10 9 = - 8 . 7 × 10 9 J

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Important Questions on Gravitation

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Science>Physics>Gravitation>Escape Velocity

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

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Science>Physics>Gravitation>Escape Velocity

Define escape speed. Derive an expression for the escape speed of an object from the surface of the each.

HARD

Science>Physics>Gravitation>Escape Velocity

Show that the sum of the kinetic energy and potential energy of a freely falling body is conserved?

HARD

Science>Physics>Gravitation>Escape Velocity

A satellite orbits the earth at a height of

500 km

from its surface. Calculate potential energy.

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Science>Physics>Gravitation>Escape Velocity

Identify whether the statement is right or wrong. Rewrite the statement by making necessary corrections.
When a body is falling freely from a height, its kinetic energy remains constant.

MEDIUM

Science>Physics>Gravitation>Escape Velocity

On which factors does the escape speed of a body from the surface of earth depends?

HARD

Science>Physics>Gravitation>Escape Velocity

A planet or a satellite is revolving round the sun or earth. Calculate its kinetic, potential and total energy. Explain the significance of these values. Draw graphs to show the variations of these with distance

r

from the sun or the earth. Explain the curves.

HARD

Science>Physics>Gravitation>Escape Velocity

Two inclined frictionless tracks, one gradual and the other steep meet at A, from where two stones are allowed to slide down from rest, one on each track (Figure). Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given

θ_{1} = 30 °, θ_{2} = 60 °

, and

h = 10 m

, what are the speeds and times taken by the two stones?
Question Image

MEDIUM

Science>Physics>Gravitation>Escape Velocity

Draw a diagram to show conservation of mechanical energy in case of a free-falling body.

MEDIUM

Science>Physics>Gravitation>Escape Velocity

U -

shaped smooth wire has a semi-circular bend of radius

R

between

A

and

B

. It is held fixed in a vertical plane. A bead of mass

m

is released from height

h

(above

A

) and slides smoothly along the wire to reach the same height on other side of the wire. It is given that

h ≫ R

Consider the motion of the bead between

A

and the lowest point

C

of the wire. The ratio of change in magnitude of velocity of the particle at

A

to the magnitude of change in its velocity at

C

is nearly equal to

HARD

Science>Physics>Gravitation>Escape Velocity

A satellite orbits the earth at a height of

500 km

from its surface. Calculate total energy. Mass of the satellite is

300 kg

, mass of the earth is

6 \times 10^{24} kg

, radius of the earth is

6.4 \times 10^{6} m

and

G

6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2}

. Will your answer alter if the earth were to shrink suddenly to half its size ?

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Science>Physics>Gravitation>Escape Velocity

When an apple falls from a tree, what happens to its gravitational potential energy:

i. Just as it reaches the ground?

ii. After it strikes the ground?

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Science>Physics>Gravitation>Escape Velocity

What is escape velocity of a satellite?

HARD

Science>Physics>Gravitation>Escape Velocity

A satellite orbits the earth at a height of

500 km

from its surface. Calculate kinetic energy

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Science>Physics>Gravitation>Escape Velocity

Are kinetic and potential energies interconvertible?

HARD

Science>Physics>Gravitation>Escape Velocity

If the earth were made of wood, the mass of wooden earth would have been 10% as much as it is now(without change in its diameter). Calculate escape speed from the surface of this earth.

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Science>Physics>Gravitation>Escape Velocity

State with reasons whether the following sentences are true or false.
If a spacecraft has to be sent away from the influence of earth’s gravitational field, its velocity must be less than the escape velocity.

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Science>Physics>Gravitation>Escape Velocity

From where the kinetic energy of the falling rain drop come?

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Science>Physics>Gravitation>Escape Velocity

State if the given statement is true or false. Give reasons for your answer.

Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

MEDIUM

Science>Physics>Gravitation>Escape Velocity

If a body is thrown upward with a velocity of

11.2 km s^{- 1}

what will happen?

Write a short note on escape velocity.

Important Questions on Gravitation

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