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Question (1)

QN0035481

A satellite is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

(A)
the total mechanical energy of varies periodically with time.
(B)
the linear momentum of remains constant in magnitude.
(C)
the acceleration of S is always directed towards the centre of the earth.
(D)
the angular momentum of about the centre of the earth changes in direction, but its magnitude remains constant.

Correct Answer: C

Explanation:

The gravitational force on the satellite will be aiming towards the centre of the earth so acceleration of the satellite will also be aiming towards the centre of the earth.

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Question (2)

QN0035482

A remote - sensing satellite of earth revolves in a circular orbit at a height of above the surface of earth. If earth's radius is and , then the orbital speed of the satellite is:

(A)
(B)
(C)
(D)

Correct Answer: D

Explanation:

Given: Height of the satellite from the earth's surface

Radius of the earth

Acceleration due to gravity

Orbital velocity, ?

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Question (3)

QN0035483

The ratio of escape velocity at earth to the escape velocity at a planet whose radius and mean density are twice as that of earth is:

(A)
(B)
(C)
(D)

Correct Answer: B

Explanation:

As we know, escape velocity,

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Question (4)

QN0035484

At what height from the surface of earth the gravitational potential and the value of are and 6.0 respectively? Take the radius of earth as :

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

As we know, gravitational potential (v) and acceleration due to gravity with height

Dividing (i) by (ii)

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Question (5)

QN0035485

The acceleration due to gravity at a height above the earth is the same as at a depth below the surface of earth. Then

(A)
(B)
(C)
(D)

Correct Answer: C

Explanation:

Above earth surface. Below earth surface

According to question,

Clearly,

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Question (6)

QN0035486

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions and are and , respectively. is the major axis and is perpendicular to at the position of the Sun as shown in the figure. Then

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

Speed of the planet will be maximum when its distance from the sun is minimum as constant.

Point is perihelion and is aphelion.

Clearly,

So,

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Question (7)

QN0035487

The work done to raise a mass from the surface of the earth to a height , which is equal to the radius of the earth, is

(A)
(B)
(C)
(D)

Correct Answer: C

Explanation:

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Question (8)

QN0035488

A body weighs on the surface of the earth. How much will it weigh half way down to the centre of the earth?

(A)
(B)
(C)
(D)

Correct Answer: D

Explanation:

Acceleration due to gravity at a depth from surface of earth

Here,

Multiplying by mass ' ' on both sides of equation (i) we get

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Question (9)

QN0035489

A body weighs on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

Weight of a body on the surface of the earth,
Acceleration due to gravity, varies with height,

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Question (10)

QN0035490

The escape velocity from the Earth's surface is . The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

Escape velocity from the earth's surface

or, or, same density

or,

Escape velocity is double if the radius of the earth is double keeping the density unchanged. Escape velocity depends on the mass and size of the planet.

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Question (1)

A satellite is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

Explanation:

Link:

Question (2)

A remote - sensing satellite of earth revolves in a circular orbit at a height of above the surface of earth. If earth's radius is and , then the orbital speed of the satellite is:

Explanation:

Link:

Question (3)

The ratio of escape velocity at earth to the escape velocity at a planet whose radius and mean density are twice as that of earth is:

Explanation:

Link:

Question (4)

At what height from the surface of earth the gravitational potential and the value of are and 6.0 respectively? Take the radius of earth as :

Explanation:

Link:

Question (5)

The acceleration due to gravity at a height above the earth is the same as at a depth below the surface of earth. Then

Explanation:

Link:

Question (6)

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions and are and , respectively. is the major axis and is perpendicular to at the position of the Sun as shown in the figure. Then

Explanation:

Link:

Question (7)

The work done to raise a mass from the surface of the earth to a height , which is equal to the radius of the earth, is

Explanation:

Link:

Question (8)

A body weighs on the surface of the earth. How much will it weigh half way down to the centre of the earth?

Explanation:

Link:

Question (9)

A body weighs on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

Explanation:

Link:

Question (10)

The escape velocity from the Earth's surface is . The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

Explanation:

Link:

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