Gravitation Test

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Gravitation Test - 36

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Question 1
1 / -0

If the distance between two objects is doubled , the gravitation force between them

A
remains the same

B
gets doubled

C
gets halved

D
becomes one-fourth

Solution

If the distance between two objects is doubled the gravitational force becomes one fourth since,

$$ F = G \dfrac{m_1 \times m_2}{R^2} $$

Where $$ R $$ is the diatnce between the bodies .

So , if $$ R' = 2R $$ , then

$$ F ' = G \dfrac{m_1 \times m_2}{R'^2} $$

$$ F ' = G \dfrac{m_1 \times m_2}{4 \times R^2} = \dfrac{F}{4} $$
Question 2
1 / -0

The value of gravitational constant depends upon :

A
temperature of the atmosphere

B
masses

C
distance between the masses

D
none of these

Solution

The gravitational constant is a universal constant. It remains as it is in any condition.
It does not depend on any of the factors like the temperature, mass, distance between the masses.

Value of G is $$ 6.67 \times 10^{-11} \, Nm^2 kg^{-2} $$
Question 3
1 / -0

The force of buoyancy is equal to:

A
Weight of the body

B
Weight of the liquid displaced by the body

C
Apparent weight of the body

D
None of these

Solution

According to Archimedes’ principle, when a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it. The upward force exerted by the liquid on the body is known as upthrust or buoyant force.
Question 4
1 / -0

A body projected vertically upwards with a velocity of $$19.6\; ms^{-1}$$ reaches a height of $$19.6\; m$$ on earth. If it is projected vertically up with the same velocity on moon, then the maximum height reached by it is ($$g_{earth}=g \ ms^{-2}$$, $$g_{moon}=\dfrac{g}{6}\ ms^{-2}$$)

A
19.18 m

B
3.3 m

C
9.9 m

D
117.6 m

Solution

$$v^2 = u^2 - 2gs \Rightarrow s = \dfrac {u^2}{2g}$$
$$v = 0$$ for maximum height.

On moon, $$ g' = \dfrac {g}{6}$$
Hence $$s' = \dfrac {s}{\dfrac {1}{6}} = 6s = 6 \times 19.6 = 117.6 \;m$$
Question 5
1 / -0

The weight of the body is maximum in:

A
air

B
hydrogen

C
water

D
vacuum
Solution
Hint: The net weight of a body depends on both gravitational and buoyant force.

Correction Option: D

Explanation for correct answer:
- According to Archimedes’ principle, when a body is immersed in a fluid completely or partially, there is some loss in weight of the body due to buoyant force action on the opposite direction of gravitational force.
- So, the weight of the body is = Gravitational force - Buoyant force
- In vacuum, there will be no buoyant force.
So, the weight of a body will be maximum in vacuum.
Question 6
1 / -0

Two particles are placed at some distance and the magnitude of gravitational force between them is F. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the new value of gravitational force, in terms of F, between them will be:

A
$$\dfrac{F}{4} $$

B
$$4F $$

C
$$\dfrac{F}{2} $$

D
$$F$$

Solution

The force of gravitational attraction between the two bodies of mass ($$M$$) and ($$m$$) is $$F= G\frac{Mm}{r^{2}}$$.
Now, If masses of both objects are halved without changing distance between them or $$M =2M$$ and $$2m$$
Now, $$F= G\dfrac{2M \times 2m}{ r^{2}}=4G\dfrac{Mm}{ r^{2}}$$.
Thus, force becomes four times as we increase the masses to double without altering the distances.
Question 7
1 / -0

The gravitational force between two objects is F. If masses of both objects are halved without changing distance between them, then the gravitational force would become:

A
F/4

B
F/2

C
F

D
2 F

Solution

The force of gravitational attraction between the two bodies of mass ($$M$$) and ($$m$$) is $$F= G\frac{Mm}{r^{2}}$$.
Now, If masses of both objects are halved without changing distance between them or $$M =\frac{M}{2}$$ and $$m=\frac{m}{2}$$
Now, $$F= G\frac{Mm}{4 r^{2}}$$.
Thus, force becomes one-fourth as we reduce the masses to half without altering the distances.
Question 8
1 / -0

Consider the following two statements and identify the correct choice.
A: When a body floats in a liquid, it displaces the liquid whose weight is equal to its own weight.
B: When a body sinks in a liquid, it displaces the liquid whose volume is equal to its own volume.

A
A is true but B is false

B
Both A and B are true

C
A is false but B is true

D
Both A and B are false.

Solution

Displacement is pushing an object out of the way and taking its place when it is dipped in a fluid. When a body sinks in a liquid, it displaces an amount of fluid equal to its own volume. When a body floats in a liquid, it displaces an amount of fluid equal to its own weight.
Hence according to Archimedes' principle, which is a physical law of buoyancy, the amount of fluid displaced is directly related to its volume. The principle states that any body completely or partially submerged in a liquid is acted upon by a buoyant force, the magnitude of which is equal to the weight of the fluid displaced by the body.
Thus, the correct answer is option B.
Question 9
1 / -0

A hydrogen balloon released on the moon would :

A
Climb up with an acceleration of $$98\ m/\ sec^{2}$$

B
Climb up with an acceleration of $$9.8\times 6m/sec^{2}$$

C
Neither climb nor fall

D
Fall with an acceleration of $$(9.8/6)m/\ sec^{2}$$

Solution

The gravity on moon is approximately 6 times as less as that of the earth and due to lack of atmosphere, the only force acting on the balloon is the gravitational force of the moon. Hence, the balloon descends with an acceleration of $$\dfrac{9.8}{6}m/s^2$$.
Question 10
1 / -0

An astronaut standing on the surface of the moon throws a ball upwards. The ball would:

A
directly fall down from the point it is released

B
hang in space

C
go up and then come back to the surface of the moon

D
keep going up never to come back

Solution

The acceleration due to gravity on the surface of the Moon is 1.62519(412) $$m/{ s }^{ 2 }$$, about 16.6% that on Earth's surface. Over the entire surface, the variation in gravitational acceleration is about 0.0253 $$m/{ s }^{ 2 }$$ (1.6% of the acceleration due to gravity). Because weight is directly dependent upon gravitational acceleration, things on the Moon will weigh only 16.6% of what they weigh on the Earth.
Hence, the ball will go up and then come back to the surface of the moon.

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Gravitation Test - 36

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Gravitation Test - 36

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Question 1

remains the same

gets doubled

gets halved

becomes one-fourth

Solution

Question 2

temperature of the atmosphere

masses

distance between the masses

none of these

Solution

Question 3

Weight of the body

Weight of the liquid displaced by the body

Apparent weight of the body

None of these

Solution

Question 4

19.18 m

3.3 m

9.9 m

117.6 m

Solution

Question 5

air

hydrogen

water

vacuum

Solution

Question 6

$$\dfrac{F}{4} $$

$$4F $$

$$\dfrac{F}{2} $$

$$F$$

Solution

Question 7

F/4

F/2

F

2 F

Solution

Question 8

A is true but B is false

Both A and B are true

A is false but B is true

Both A and B are false.

Solution

Question 9

Climb up with an acceleration of $$98\ m/\ sec^{2}$$

Climb up with an acceleration of $$9.8\times 6m/sec^{2}$$

Neither climb nor fall

Fall with an acceleration of $$(9.8/6)m/\ sec^{2}$$

Solution

Question 10

directly fall down from the point it is released

hang in space

go up and then come back to the surface of the moon

keep going up never to come back

Solution

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