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This mock test of Central Forces NAT Level – 1 for IIT JAM helps you for every IIT JAM entrance exam.
This contains 10 Multiple Choice Questions for IIT JAM Central Forces NAT Level – 1 (mcq) to study with solutions a complete question bank.
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*Answer can only contain numeric values

QUESTION: 1

The change in the value of * g* at a height

Solution:

The gravitational field inside the earth is given by where r is the distance from centre

The correct answer is: 2

*Answer can only contain numeric values

QUESTION: 2

Energy required to move a body of mass * m * from an orbit of radius

Solution:

The correct answer is: 12

*Answer can only contain numeric values

QUESTION: 3

A satellite in a circular orbit of radius * r* has time period of 4

Solution:

Radius of orbit of the first satellite

R_{1} = R

Time period of the first satellite T = 4 hrs. and radius of orbit of second satellite = 4r

The time period of satellite is given by

The correct answer is: 32

*Answer can only contain numeric values

QUESTION: 4

The minimum and maximum distances of a satellite from the centre of earth are **2 R** and

Solution:

Applying conservation of angular momentum

From conservation of energy

Solving Eqs. (1) and (2), we get

If *r* is the radius of curvature at point *A
*

The correct answer is: 2.667

*Answer can only contain numeric values

QUESTION: 5

Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from Earth’s surface is R/α. Find the value of α.

Solution:

Applying energy conservation

The correct answer is: 3

*Answer can only contain numeric values

QUESTION: 6

Two satellites ** S_{1}** and

Solution:

V=√(GM/r)

⇒ V_{1}/V_{2 }= (4/1)^{1/2}

⇒ V_{1}/V_{2} = 2/1

*Answer can only contain numeric values

QUESTION: 7

Radius of the earth is * R* and the means density is ρ. Find out the gravitational potential at the earth’s surface απGρR

Solution:

The correct answer is: -1.333

*Answer can only contain numeric values

QUESTION: 8

A body which is initially at rest at a height * R* above the surface of the earth of radius

Take * g *= 10

Solution:

Potential energy at ground surface

Potential energy

potential energy at a height of R is

potential energy

When a body comes to ground

Loss in potential energy = Gain in kinetic energy

The correct answer is: 8000

*Answer can only contain numeric values

QUESTION: 9

A particle is projected from the surface of earth with an initial speed of 4.0*km/s*. Find the maximum height (in *kms*) attained by the particle.

Solution:

Radius of earth = 6400*km* and the maximum height attained by the particle is, and * g* = 9.8

Substituting the value,

or h = 935km

The correct answer is: 935

*Answer can only contain numeric values

QUESTION: 10

The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is V_{0}. The value of orbital velocity for another satellite orbiting at an altitude of half of earth’s radius is Find the value of α.

Solution:

For first satellite

For second satellite

The correct answer is: 0.667

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