Gravitation Test

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Gravitation Test - 59

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Question 1
1 / -0

The radius of Earth is about $$6400 \ km$$ and that of mars is $$3200 \ km $$. The mass of earth is $$10$$ times that of mars. An object weighs $$200 \ N$$ on the surface of Earth. Its weight on the surface of Mars will be:-

A
$$80 \ N$$

B
$$40 \ N$$

C
$$20 \ N$$

D
$$8 \ N$$

Solution
Question 2
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For two balls of equal mass as shown in the figure, the magnitude of gravitational force between them if $$F$$. In which of the conditions shown in the options, the gravitational force remains same i.e., F?

A

B

C

D
Question 3
1 / -0

The value of universal gravitational constant $$'G'$$ was first experimentally determined by :

A
Galileo

B
Newton

C
Cavendish

D
Kelvin

Solution

Cavendish experiment . The Cavendish experiment , performed in 1797–1798 by British scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate value for the gravitational constant
Hence,
option $$C$$ is correct answer.
Question 4
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If the distance between two bodies is doubled, the force of gravitational attraction between them.

A
Becomes four times

B
Is doubled

C
Is reduced to one-fourth

D
Is reduced to half.

Solution
Question 5
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The gravitational force between two point masses $${ m }_{ 1 }$$ and $${ m }_{ 2}$$ at separation r is given by
$$F=k\dfrac { { m }_{ 1 }{ m }_{ 2 } }{ { r }^{ 2 } } .$$
The constant k depends on :

A
Depends on system of units only

B
Depends on medium between masses only

C
Depends on both (a) and (b)

D
is independent of both (a) and (b)

Solution
Question 6
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Regarding weight(w) which is correct?

A
value changes with g

B
At centre of the earth weight is maximum

C
It unit is kg-wt

D
It is scalar quantity

Solution

It unit is $$k g-wt$$.
$$1kg-wt= 9.8N$$
Option $$C$$ is correct statement.
Question 7
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The mass of the moon is $$7.34 \times {10^{22}}kg$$ and the radius is $$1.74 \times {10^6}m$$ . value of gravitational acceleration will be

A
$$1.45 \ N/kg$$

B
$$1.55 \ N/kg$$

C
$$1.75 \ N/kg$$

D
$$1.62 \ N/kg$$

Solution

Given:
$$M_m=7.34 \times {10^{22}}kg\\R_m=1.74 \times {10^6}m$$

$$g=\dfrac{GM}{R^2}= \dfrac{6.67 \times 10^{-11} \times 7.34 \times 10^{22}}{(1.74 \times 10^6)^2}= 1.62 \ N/kg$$
Question 8
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Weight is defined as

A
Force of attraction exerted by the earth

B
Mass of a body

C
Nature of a body

D
None of these

Solution

The weight of an object is defined as the force of gravitational attraction on the object by earth and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton.
Question 9
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Calculate the force of gravitation between the earth and the sun, given that the mass of the earth $$= 6\times 10^{24}\, kg$$ and of the sun $$= 2\times 10^{30}\, kg$$. The average distance between the two is $$1.5\times 10^{11}m$$.

A
$$4.56\times 10^{22}N$$

B
$$3.56\times 10^{22}N$$

C
$$2.56\times 10^{22}N$$

D
$$5.56\times 10^{22}N$$

Solution
Question 10
1 / -0

An astronaut in a space station orbits above the Earth. In the space station, the acceleration due to gravity is $$7.5\ m / s^{2}$$. On Earth, the acceleration due to gravity is $$10\ m / s^{2}$$.
Which statement about the astronaut’s mass and weight in the space station is correct?

A
Mass of astronaut - Same as on the Earth, weight of astronaut - less than the weight on the Earth

B
Mass of astronaut - Same as on the Earth, weight of astronaut - greater than the weight on the Earth

C
Mass of astronaut - lower than as on the Earth, weight of astronaut - less than the weight on the Earth

D
Mass of astronaut - lower than as on the Earth, weight of astronaut - greater than the weight on the Earth

Solution

Since Mass is the property of the body so it remains the same.
Weight $$W=mg$$ , where g is the acceleration due to gravity at that place.
It is clear from the question that, $$g_{earth} > g_{space\ station}$$
So $$W_{earth} > W_{space\ station}$$