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IIT JAM Exam > IIT JAM Tests > Central Forces NAT Level – 1 - IIT JAM MCQ

Central Forces NAT Level – 1 - IIT JAM MCQ

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10 Questions MCQ Test - Central Forces NAT Level – 1

Central Forces NAT Level – 1 for IIT JAM 2024 is part of IIT JAM preparation. The Central Forces NAT Level – 1 questions and answers have been prepared according to the IIT JAM exam syllabus.The Central Forces NAT Level – 1 MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Central Forces NAT Level – 1 below.

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*Answer can only contain numeric values

Central Forces NAT Level – 1 - Question 1

The change in the value of g at a height h above the surface of the earth is the same as at a depth d below that surface of earth. When both d and h are much smaller than the radius of earth, then, d = αh. Find the value of α.

Detailed Solution for Central Forces NAT Level – 1 - Question 1

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

Central Forces NAT Level – 1 - Question 2

Energy required to move a body of mass m from an orbit of radius 2R to 3R is Find the value of α

Detailed Solution for Central Forces NAT Level – 1 - Question 2

The correct answer is: 12

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*Answer can only contain numeric values

Central Forces NAT Level – 1 - Question 3

A satellite in a circular orbit of radius r has time period of 4hrs. A satellite with orbital radius of 4r around the same planet will have a time period of in hours.

Detailed Solution for Central Forces NAT Level – 1 - Question 3

Radius of orbit of the first satellite

R₁ = 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

Central Forces NAT Level – 1 - Question 4

The minimum and maximum distances of a satellite from the centre of earth are 2R and 4R respectively, where R is the radius of earth and M is the mass of the earth. The radius of curvature at the point of minimum distance is λR. Find the value of λ.

Detailed Solution for Central Forces NAT Level – 1 - Question 4

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

Central Forces NAT Level – 1 - 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.

Detailed Solution for Central Forces NAT Level – 1 - Question 5

Applying energy conservation

The correct answer is: 3

*Answer can only contain numeric values

Central Forces NAT Level – 1 - Question 6

Two satellites S₁ and S₂ of equal masses revolves in the same sense around a heavy planet in coplanar circular orbit of radii R and 4R. Find the value of

Detailed Solution for Central Forces NAT Level – 1 - Question 6

V=√(GM/r)
⇒ V₁/V₂= (4/1)^1/2
⇒ V₁/V₂ = 2/1

*Answer can only contain numeric values

Central Forces NAT Level – 1 - Question 7

Radius of the earth is R and the means density is ρ. Find out the gravitational potential at the earth’s surface απGρR². Find the value of α.

Detailed Solution for Central Forces NAT Level – 1 - Question 7

The correct answer is: -1.333

*Answer can only contain numeric values

Central Forces NAT Level – 1 - Question 8

A body which is initially at rest at a height R above the surface of the earth of radius R, falls freely towards the earth. Find out its velocity (in m/s) on reaching the surface of earth.

Take g = 10m/s² and R = 6400km.

Detailed Solution for Central Forces NAT Level – 1 - Question 8

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

Central Forces NAT Level – 1 - Question 9

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

Detailed Solution for Central Forces NAT Level – 1 - Question 9

Radius of earth = 6400km and the maximum height attained by the particle is, and g = 9.8 m/s².
Substituting the value,

or h = 935km
The correct answer is: 935

*Answer can only contain numeric values

Central Forces NAT Level – 1 - Question 10

The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is V₀. The value of orbital velocity for another satellite orbiting at an altitude of half of earth’s radius is Find the value of α.

Detailed Solution for Central Forces NAT Level – 1 - Question 10

For first satellite

For second satellite

The correct answer is: 0.667

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