Gravitation Test

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Gravitation Test - 13

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Question 1
1 / -0

If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect?

A
Viscous forces

B
Archimede's uplift as it depends on the weight of the body

C
Electrostatic force

D
None of the above

Solution

Archimedes uplift as it depends on the weight of the body.
Question 2
1 / -0

A satellite of the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly disappears, the satellite will

A
Continue to move with velocity v along the original orbit

B
Move with a velocity v, tangentially to the original orbit

C
Fall down with increasing velocity

D
Ultimately come to rest somewhere on the original orbit

Solution

Due to inertia of direction.
Question 3
1 / -0

If the distance between two masses is doubled, the gravitational attraction between them

A
Is doubled

B
Becomes four times

C
Is reduced to half

D
Is reduced to a quarter

Solution

\(F \propto \frac{1}{r^2}\)

If r becomes double then F reduces to \(\frac{F}{4}\)
Question 4
1 / -0

The centripetal force acting on a satellite orbiting round the earth and the gravitational force of earth acting on the satellite both equal F. The net force on the satellite is

A
Zero

B
F

C
\(F \sqrt 2\)

D
2F

Solution

Actually gravitational force provides the centripetal force.
Question 5
1 / -0

The time period of a simple pendulum on a freely moving artificial satellite is

A
Zero

B
2 sec

C
3 sec

D
Infinite

Solution

Time period of simple pendulum

T = \(2\pi \sqrt{\frac{l}{g'}}\)

In artificial satellite g′ = 0 and

\(\therefore\,T\) = infinite.
Question 6
1 / -0

A body of mass m is taken to the bottom of a deep mine. Then

A
Its mass increases

B
Its mass decreases

C
Its weight increases

D
Its weight decreases

Solution

Because acceleration due to gravity decreases
Question 7
1 / -0

In order to find time, the astronaut orbiting in an earth satellite should use

A
A pendulum clock

B
A watch having main spring to keep it going

C
Either a pendulum clock or a watch

D
Neither a pendulum clock nor a watch

Solution

In pendulum clock the time period depends on the value of g, while in spring watch, the time period is independent of the value of g.
Question 8
1 / -0

The weight of an object in the coal mine, sea level, at the top of the mountain is \(W_1, W_2\) and \(W_3\) respectively, then

A
\(W_1< W_2 > W_3\)

B
\(W_1= W_2 = W_3\)

C
\(W_1< W_2 < W_3 \)

D
\(W_1> W_2 > W_3\)

Solution

Because value of g decreases when we move either in coal mine or at the top of mountain.
Question 9
1 / -0

The mass of the earth is 81 times that of the moon and the radius of the earth is 3.5 times that of the moon. The ratio of the acceleration due to gravity at the surface of the moon to that at the surface of the earth is

A
0.15

B
0.04

C
1

D
6

Solution

g = \(\frac{GM}{R^2}\)

Given \(M_e\) = 81 \(M_m\), \(R_e\) = 3.5 \(R_m\)) Substituting the above values, \(\frac{g_m}{g_e}\) = 0.15
Question 10
1 / -0

In a gravitational field, at a point where the gravitational potential is zero

A
The gravitational field is necessarily zero

B
The gravitational field is not necessarily zero

C
Nothing can be said definitely about the gravitational field

D
None of these

Solution

I = \(-\frac{dV}{dx} \)

If V = 0 then gravitational field is necessarily zero.
Question 11
1 / -0

There are two bodies of masses 100 kg and 10000 kg separated by a distance 1m. At what distance from the smaller body, the intensity of gravitational field will be zero

A
\(\frac{1}{9}m\)

B
\(\frac{1}{10}m\)

C
\(\frac{1}{11}m\)

D
\(\frac{10}{11}m\)

Solution

\(\frac{G \times 100}{x^2}\) = \(\frac{G \times 10000}{(1 - x)^2}\)

⇒ \(\frac{10}{x} = \frac{100}{1 - x}\)

⇒ x = \(\frac{1}{11}m\)
Question 12
1 / -0

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional

A
\(\frac{1}{R}\)

B
\(\frac{1}{\sqrt R}\)

C
R

D
\(\frac{1}{R^{\frac{3}{2}}}\)

Solution

K.E. = \(\frac{GMm}{2R}\)
Question 13
1 / -0

Select the correct statement from the following :

A
The orbital velocity of a satellite increases with the radius of the orbit.

B
Escape velocity of a particle from the surface of the earth depends on the speed with which it is fired.

C
The time period of a satellite does not depend on the radius of the orbit.

D
The orbital velocity is inversely proportional to the square root of the radius of the orbit.

Solution

\(v_0 = \sqrt{\frac{GM}{r}}\)
Question 14
1 / -0

Consider a satellite going round the earth in an orbit. Which of the following statements is wrong?

A
It is a freely falling body

B
It suffers no acceleration

C
It is moving with a constant speed

D
Its angular momentum remains constant

Solution

Centripetal acceleration works on it.
Question 15
1 / -0

Assertion: Gravitational force between two particles is negligibly small compared to the electrical force.

Reason: The electrical force is experienced by charged particles only.

(A) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(C) If assertion is true but reason is false.

(D) If the assertion and reason both are false.

A
A

B
B

C
C

D
D

Solution

For two-electron \(\frac{F_g}{F_e} = 10^{-43}\) i.e. gravitational force is negligible in comparison to electrostatic force of attraction.
Question 16
1 / -0

If the earth is at one-fourth of its present distance from the sun, the duration of the year will be

A
Half the present year

B
One-eighth the present year

C
One-fourth the present year

D
One-sixth the present year

Solution

Since \(T^2 \propto r^3\)

\(\therefore \Big(\frac{T'}{T} \Big)^2 = \Big(\frac{1}{4} \Big)^3 \)

⇒ T' = \(\frac{1}{8}T\)
Question 17
1 / -0

The earth revolves about the sun in an elliptical orbit with mean radius \(9.3 ×10^7\) m in a period of 1 year. Assuming that there are no outside influences

A
The earth's kinetic energy remains constant

B
The earth's angular momentum remains constant

C
The earth's potential energy remains constant

D
All are correct

Solution

Kinetic and potential energies vary with position of earth w.r.t. sun. Angular momentum remains constant everywhere.
Question 18
1 / -0

As observed from the earth, the sun appears to move in an approximately circular orbit. For the motion of another planet like mercury as observed from the earth, this would

A
Be similarly true

B
Not be true because the force between the earth and mercury is not inverse square law

C
Not be true because the major gravitational force on mercury is due to the sun

D
Not be true because mercury is influenced by forces other than gravitational forces

Solution

As observed from the earth, the sun appears to move in an approximate circular orbit. The gravitational force of attraction between the earth and the sun always follows inverse square law. Due to relative motion between the earth and mercury, the orbit of mercury, as observed from the earth, will not be approximately circular, since the major gravitational force on mercury is due to the sun.
Question 19
1 / -0

A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is

A
Positive

B
Negative

C
Zero

D
May be positive or negative depending upon its initial velocity

Solution

At earth, total energy of the missile is \(\frac{1}{2}mv^2 - \frac{GmR}{r}\)

Where, mm is the mass of the missile, vv is the velocity of the missile at a distance rr from the earth, RR is the radius of earth. Now to escape the gravitational pull of earth, this total energy should be greater than zero or equal to zero (energy at infinity), i.e.

\(\frac{1}{2}mv^2 - \frac{GmR}{r} \geq 0\)
Question 20
1 / -0

For the moon to cease to remain the earth's satellite, its orbital velocity has to increase by a factor of

A
2

B
\(\sqrt 2\)

C
\(\frac{1}{\sqrt 2}\)

D
\(\sqrt 3\)

Solution

\(V_e = \sqrt 2 v_0\)

i.e. if the orbital velocity of moon is increased by factor of \(\sqrt 2\) then it will escape out from the gravitational field of earth.

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Re-Attempt Weekly Quiz Competition

Gravitation Test - 13

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Gravitation Test - 13

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SHARING IS CARING

Question 1

Viscous forces

Archimede's uplift as it depends on the weight of the body

Electrostatic force

None of the above

Solution

Question 2

Continue to move with velocity v along the original orbit

Move with a velocity v, tangentially to the original orbit

Fall down with increasing velocity

Ultimately come to rest somewhere on the original orbit

Solution

Question 3

Is doubled

Becomes four times

Is reduced to half

Is reduced to a quarter

Solution

Question 4

Zero

F

\(F \sqrt 2\)

2F

Solution

Question 5

Zero

2 sec

3 sec

Infinite

Solution

Question 6

Its mass increases

Its mass decreases

Its weight increases

Its weight decreases

Solution

Question 7

A pendulum clock

A watch having main spring to keep it going

Either a pendulum clock or a watch

Neither a pendulum clock nor a watch

Solution

Question 8

\(W_1< W_2 > W_3\)

\(W_1= W_2 = W_3\)

\(W_1< W_2 < W_3 \)

\(W_1> W_2 > W_3\)

Solution

Question 9

0.15

0.04

1

6

Solution

Question 10

The gravitational field is necessarily zero

The gravitational field is not necessarily zero

Nothing can be said definitely about the gravitational field

None of these

Solution

Question 11

\(\frac{1}{9}m\)

\(\frac{1}{10}m\)

\(\frac{1}{11}m\)

\(\frac{10}{11}m\)

Solution

Question 12

\(\frac{1}{R}\)

\(\frac{1}{\sqrt R}\)

R

\(\frac{1}{R^{\frac{3}{2}}}\)

Solution