Description

This mock test of Central Forces MSQ for IIT JAM helps you for every IIT JAM entrance exam.
This contains 10 Multiple Choice Questions for IIT JAM Central Forces MSQ (mcq) to study with solutions a complete question bank.
The solved questions answers in this Central Forces MSQ quiz give you a good mix of easy questions and tough questions. IIT JAM
students definitely take this Central Forces MSQ exercise for a better result in the exam. You can find other Central Forces MSQ extra questions,
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*Multiple options can be correct

QUESTION: 1

Three point masses, *m* each are at the corners of an equilateral triangle of side *a.* Their separations do not change when the system rotates about the centre of the triangle. For this, the time period of rotation must be proportional to :

Solution:

The correct answers are: *a*^{3/2}, *m*^{–1/2}

*Multiple options can be correct

QUESTION: 2

A solid sphere of uniform density and radius 4*units* is located with its centre at the origin of coordinates, *O*. Two spheres of equal radii of 1*unit*, with their centres at *A***(-2,0,0)** and **B****(2, 0, 0)** respectively, are taken out of the solid sphere, leaving behind spherical cavities as shown in the figure.

Solution:

Use arguments of symmetry as the *yz* plane divides the objects symmetrically.

The correct answers are: The gravitational force due to this object at the origin is zero, The gravitational potential is the same at all points of the circle *y*^{2} + *z*^{2} = 36, The gravitational potential is the same at all points of the circle *y*^{2} + *z*^{2} = 4

*Multiple options can be correct

QUESTION: 3

A satellite revolves around a planet in circular orbit of radius * R *(much larger than the radius of the planet) with a time period of revolution

Solution:

It will fall because mg is acting on it towards the centre of planet and initial velocity is zero. It’ll move in straight line.

By energy conservation

using this we get V = f(r)

Now use

*R'* = radius of the planet.

In the final expression (on in the beginning itself)

The correct answers are: It will fall on the planet, The time of fall of the satellite on the planet is nearly

*Multiple options can be correct

QUESTION: 4

Let * V* and

Solution:

A) At ∞ both V and E are zero.

B) Let, V_{∞}=GM/R for an unit mass.

So, V_{R}=0 i.e. at the radius R of solid sphere(mass M) and E_{R}=GM/R^{2}

C) Inside a spherical shell V =GM/R and E =0

Thus, all the above are correct.

*Multiple options can be correct

QUESTION: 5

A small mass * m* is moved slowly from the surface of the earth to a height

Solution:

For, h<<R force is constant and is equal to mg

**Therefore, work done is mgh in moving by distance h**

For, h=R

gravitational potential at x is − GM/x

Work done in moving from x=R to x=2R is − GMm/2R + GMm/R

= GMm/2R

**which is equal to 1/2 mgR**

*Multiple options can be correct

QUESTION: 6

A satellite close to the earth is in orbit above the equator with the period of rotation of 1.5*hours*. If it is above a point *P* on the equator at some time, it will be above *P* again after time :

Solution:

Let ω_{0} = the angular velocity of the earth about its axis.

Let ω = the angular velocity of the satellite

For a satellite rotating from west to east (the same as the earth), the relative angular velocity, ω_{1} = ω - ω_{0}

The period of rotation relative to the earth

For a satellite rotating from east to west (opposite to the earth), the relative angular velocity, ω_{2} = ω + ω_{0}.

The correct answers are: 1.6*hours* if it is rotating from west to east, 24/17*hours* if it is rotating from east to west

*Multiple options can be correct

QUESTION: 7

The magnitudes of the gravitational field at distance r_{1} and r_{2} from the centre of a uniform sphere of radius * R* and mass

Solution:

F ∝ T, if *r* < *R*, and

if *r* > *R*.

The correct answers are:

*Multiple options can be correct

QUESTION: 8

A double star is a system of two stars of masses * m* and

Solution:

The correct answers are: ** r^{3/2}**,

*Multiple options can be correct

QUESTION: 9

A binary star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses * m* and

Solution:

The correct answers are: **l**** ^{3/2}**,

*Multiple options can be correct

QUESTION: 10

An object is weighed at the North Pole by a beam balance and a spring balance, giving readings of ** W_{B}** and

Solution:

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