Gravitation Test

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Gravitation Test - 53

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Weekly Quiz Competition

Question 1
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Two particles of mass $$m_1$$ and $$M_2$$, approach each other due to their mutual gravitational attraction only. Then

A
Accelerations of both the particles are equal

B
Accelerations of the particles of mass $$m_1$$ is proportional to $$m_1$$

C
Accelerations of the particles of mass $$m_1$$ is proportional to $$m_2$$

D
Accelerations of the particles of mass $$m_1$$ is inversely proportional to $$m_1$$

Solution

The force acting on each particle due to gravitation=$$F=\dfrac{Gm_1m_2}{r^2}$$
Acceleration of mass $$m_1=\dfrac{F}{m_1}=\dfrac{Gm_2}{r^2}$$

Acceleration of mass $$m_2=\dfrac{F}{m_2}=\dfrac{Gm_1}{r^2}$$
Hence correct answer is option C.
Question 2
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Dimensional formula of universal gravitational constant $$G$$ is-

A
$$M^{-1}L^3T^{-2}$$

B
$$M^{-1}L^2T^{-2}$$

C
$$M^{-2}L^3T^{-2}$$

D
$$M^{-2}L^2T^{-2}$$

Solution
Question 3
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Suppose that you have a mass of $$70\ kg$$. How much mass must another object have in order for your body and the other object to attract each other with a force of $$1
\ N$$ when separated by $$10\ m$$?

A
$$2.14 \times 10^{10}\ kg$$

B
$$3.14 \times 10^{10}\ kg$$

C
$$4.14 \times 10^{10}\ kg$$

D
$$1.14 \times 10^{10}\ kg$$

Solution

Given:
Mass of object-1 is $$m_1=70\ kg$$
Distance between the otwo objects $$r=10\ m$$
Gravitational force $$F=1\ N$$
Mass of object-2 is $$m_2=?$$
We know from Newton's law of gravitation that $$F=\dfrac{Gm_1m_2}{r^2}$$
$$1=\dfrac{6.67\times 10^{-11}\times 70\times m_2}{10^2}$$
$$m_2=2.14\times 10^{10} kg$$
Question 4
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If earth's radius were to hypothetically shrink by $$1\%$$, the value of $$G$$ would:

A
Shrink by $$1\%$$

B
Expand by $$1\%$$

C
Remain the same

D
Shrink by $$0.01\%$$

Solution

According to the universal law of gravitation, every object in the universe attracts every other objects with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centers of two objects.

$$F=G\dfrac{m_1m_2}{d^2}$$

where $$G$$ is the constant of proportionality and is called the universal gravitation constant. It does not depend on the radius.
So, if the earth's radius shrinks by $$1\%$$, the value of $$G$$ would remain the same.
Question 5
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The relationship between acceleration due to gravity($$g$$) and universal gravitational constant($$G$$) may be represented as:
($$M$$ and $$R$$ are the mass and radius of the earth respectively )

A
$$G = \dfrac{gM}{R^2}$$

B
$$g = \dfrac{GM}{R^2}$$

C
$$g = \dfrac{G}{R^2}$$

D
None of these

Solution

Gravitational force acting on the mass $$m$$ $$F_g = \dfrac{GMm}{R^2}$$

But $$F_g = mg$$

$$\therefore$$ $$mg = \dfrac{GMm}{R^2}$$

We get $$g = \dfrac{GM}{R^2}$$
Question 6
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How the gravitational constant will change if a brass plate is introduced between two bodies?

A
No change

B
Decreases

C
Increases

D
No sufficient data

Solution

Universal Gravitational Constant (G) remains constant irrespective of the medium between two bodies. It has a constant value of $$6.67 \times 10^{-11} Nm^{2}kg^{-2}$$
Question 7
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The moon's radius is $$\dfrac{1}{4}$$ that of the earth and its mass is $$\dfrac{1}{80}$$ times that of the earth. If $$g$$ represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

A
$$\dfrac{g}{4}$$

B
$$\dfrac{g}{5}$$

C
$$\dfrac{g}{6}$$

D
$$\dfrac{g}{8}$$

Solution

The gravitational acceleration on surface of a planet is given as:
$$g=\dfrac{GM}{R^2}$$

Hence $$\dfrac{g_m}{g_e}=\dfrac{M_m}{M_e}.\dfrac{R_e^2}{R_m^2}$$ $$=\dfrac{1}{80}.\dfrac{4^2}{1}$$ $$=\dfrac{1}{5}$$

$$\implies g_m=\dfrac{g}{5}$$
Question 8
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An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of Earth. Which of the following could explain this?

A
Both the mass and radius of the planet are twice as that of Earth.

B
Mass of the planet is half as that of Earth, but radius is same as that of Earth.

C
Both the mass and radius of the planet are half as those of Earth.

D
Radius of the planet is half as that of Earth, but the mass is the same as that of Earth.

Solution

The expression for acceleration due to gravity on the surface of a planet is given by $$g=\dfrac{GM}{R^2}.$$
if g on the other planet is double then this will be satisfied by the only condition in option C.
in option A, g on other planet is half that of the earth.
in option B, g on other planet is half that of the earth.
in option D, g on other planet is four times that of the earth.
so the best possible answer is option C.
Question 9
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Which of the following hypotheses was made by Newton?

A
Heavier body in the universe exerts a gravitational force on the lighter bodies.

B
Every body in the universe exerts a gravitational force on every other body.

C
Only the Sun gravitational force is responsible for all the motion in this universe.

D
None of the above

Solution

The law of gravitation states that the force of attraction between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between
them.
$$F_g = \dfrac{Gm_1 m_2}{r^2}$$
where $$G$$ is the gravitational constant.
Question 10
1 / -0

A bodyweight $$5 N$$ in the air and $$2 N$$ when immersed in a liquid. The buoyant force is:

A
$$2N$$

B
$$3N$$

C
$$4N$$

D
$$5N$$

Solution

Given, The weight of the body in the air is $$=5N,$$
When immersed in water, the weight of the body $$=2N$$
In water, there will be a buoyancy force Which opposes the weight of the body.
Therefore the buoyant force is equal to $$=5N-2N=3N$$

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Gravitation Test - 53

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Gravitation Test - 53

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Question 1

Accelerations of both the particles are equal

Accelerations of the particles of mass $$m_1$$ is proportional to $$m_1$$

Accelerations of the particles of mass $$m_1$$ is proportional to $$m_2$$

Accelerations of the particles of mass $$m_1$$ is inversely proportional to $$m_1$$

Solution

Question 2

$$M^{-1}L^3T^{-2}$$

$$M^{-1}L^2T^{-2}$$

$$M^{-2}L^3T^{-2}$$

$$M^{-2}L^2T^{-2}$$

Solution

Question 3

$$2.14 \times 10^{10}\ kg$$

$$3.14 \times 10^{10}\ kg$$

$$4.14 \times 10^{10}\ kg$$

$$1.14 \times 10^{10}\ kg$$

Solution

Question 4

Shrink by $$1\%$$

Expand by $$1\%$$

Remain the same

Shrink by $$0.01\%$$

Solution

Question 5

$$G = \dfrac{gM}{R^2}$$

$$g = \dfrac{GM}{R^2}$$

$$g = \dfrac{G}{R^2}$$

None of these

Solution

Question 6

No change

Decreases

Increases

No sufficient data

Solution

Question 7

$$\dfrac{g}{4}$$

$$\dfrac{g}{5}$$

$$\dfrac{g}{6}$$

$$\dfrac{g}{8}$$

Solution

Question 8

Both the mass and radius of the planet are twice as that of Earth.

Mass of the planet is half as that of Earth, but radius is same as that of Earth.

Both the mass and radius of the planet are half as those of Earth.

Radius of the planet is half as that of Earth, but the mass is the same as that of Earth.

Solution

Question 9

Heavier body in the universe exerts a gravitational force on the lighter bodies.

Every body in the universe exerts a gravitational force on every other body.

Only the Sun gravitational force is responsible for all the motion in this universe.

None of the above

Solution

Question 10

$$2N$$

$$3N$$

$$4N$$

$$5N$$

Solution

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