Gravitation Test

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Gravitation Test - 60

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Weekly Quiz Competition

Question 1
1 / -0

If the radius of the earth is reduced to half of its present value, with no change in the mass, the acceleration due to gravity will be:

A
Doubled to that of its original value

B
Four times that of its original value

C
Remains same

D
Reduced to half of its original value

Solution

The formula for the acceleration due to gravity $$(g)$$ is given as $$g=\dfrac{GM}{R^2}$$ ...........(1)
Where $$G$$ is universal gravitational constant and $$M$$ is mass of the earth with $$R$$ as the radius of the earth.
Now $$replacing$$ $$R$$ by $$R/2$$ in the equation-1
we get the new value of $$g$$ as $$g_{new}=\dfrac{GM}{R^2/4}=4\dfrac{GM}{R^2}$$
Which is $$four $$ times of its original value.
Question 2
1 / -0

Two particles are kept at a separation $$r$$. The gravitational force between them is proportional to

A
$$r$$

B
$$r^{2}$$

C
$$1/r$$

D
$$1/r^{2}$$

Solution
Question 3
1 / -0

Which statement is correct?

A
Mass is a gravitational force but weight is not a gravitational force

B
Mass is not a gravitational force and weight is not a gravitational force

C
The unit of mass is the kilogram and the unit of weight is the newton

D
The unit of mass is the newton and the unit of weight is the kilogram

Solution

As we know that mass is matter contained in a body. It is not a gravitational force. Unit of mass is kilogram$$(kg)$$

Weight is the gravitational force acting on a body and equal to $$mg$$. Unit of weight is Newton(N)
Question 4
1 / -0

On the surface of the Moon

A
The mass of an object is more but it weighs lesser

B
The mass and weight both remain unchanged

C
The mass is the same but the weight is lesser

D
The mass is more but the weight is lesser

Solution

Weight of the object on the surface of the planet.
$$W = mg$$
$$m$$; mass of the object
$$g$$; acceleration due to gravity on the surface of the planet
So weight depends upon the acceleration due to gravity while the mass of the object remains the same at every place of the universe.
Question 5
1 / -0

The gravitational force attraction between two spherical bodies, each of mass $$1\ kg$$ placed at $$10\ m$$ apart ( $$G=6.67\times 10^{-11}\ Nm^2/kg^2$$) is :

A
$$6.67\times 10^{-13}\ N$$

B
$$6.67\times 10^{-11}\ N$$

C
$$6.67\times 10^{-7}\ N$$

D
none of these

Solution
Question 6
1 / -0

The gravitational force of attraction between two spherical bodies, each of mass $$100\ kg$$, if the distance between their centres is $$100\ m$$, is :
( $$G=6.67\times 10^{-11}\ Nm^2\ kg^{-2}$$)

A
$$6.67\times 10^{-11}\ N$$

B
$$6.67\times 10^{-9}\ N$$

C
$$6.67\ N$$

D
$$none\ of\ these$$

Solution
Question 7
1 / -0

Archimedes' principle states that when a body is totally or partially immersed in a fluid, the upthrust is equal to:

A
the weight of the fluid displaced by it

B
the weight of the body

C
volume of the fluid displaced

D
volume of the body

Solution

Archimedes' principle states that:
When a body is totally or partially immersed in a fluid, the upthrust is equal to the weight of the fluid displaced by it.
Question 8
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
$$2F$$

Solution

(a) $$F/4$$
Explanation: Gravitational force between two objects varies directly as their masses and inversely as the square of the distance between them. So, when the masses of both objects are halved without changing the distance, the gravitational force between them would become one-fourth of the original value.
Question 9
1 / -0

Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be

A
$$1/4$$ times

B
$$4$$ times

C
$$1/2$$ times

D
unchanged

Solution

(b) $$4$$ times
Explanation: we know:
$$F=G \times \dfrac{m_1 \times m_2}{r^2}$$
$$F=G \times \dfrac{2m_1 \times 2m_2}{r^2}$$
$$F=4\times G \times \dfrac{m_1\times m_2}{r^2}$$
The gravitational force between two objects varies directly as their masses and inversely as the square of the distance between them. So, when the masses of both objects are doubled without changing the distance, the gravitational force between them would become four times of the original value.
Question 10
1 / -0

The unit of thrust is

A
$$ kg-f $$

B
$$ kg $$

C
$$ g $$

D
$$ m s^{-1} $$

Solution

The force acting on an object perpendicular to the surface is called thrust. Thrust per unit Area is called Pressure. .
Since thrust is also a force. Unit of thrust is defined as $$kg-f$$ or $$N$$ .
$$1$$ $$kg-f$$ is the force equal to weight of a body of mass $$1$$ $$kg$$.

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Gravitation Test - 60

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Gravitation Test - 60

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Question 1

Doubled to that of its original value

Four times that of its original value

Remains same

Reduced to half of its original value

Solution

Question 2

$$r$$

$$r^{2}$$

$$1/r$$

$$1/r^{2}$$

Solution

Question 3

Mass is a gravitational force but weight is not a gravitational force

Mass is not a gravitational force and weight is not a gravitational force

The unit of mass is the kilogram and the unit of weight is the newton

The unit of mass is the newton and the unit of weight is the kilogram

Solution

Question 4

The mass of an object is more but it weighs lesser

The mass and weight both remain unchanged

The mass is the same but the weight is lesser

The mass is more but the weight is lesser

Solution

Question 5

$$6.67\times 10^{-13}\ N$$

$$6.67\times 10^{-11}\ N$$

$$6.67\times 10^{-7}\ N$$

none of these

Solution

Question 6

$$6.67\times 10^{-11}\ N$$

$$6.67\times 10^{-9}\ N$$

$$6.67\ N$$

$$none\ of\ these$$

Solution

Question 7

the weight of the fluid displaced by it

the weight of the body

volume of the fluid displaced

volume of the body

Solution

Question 8

$$F/4$$

$$F/2$$

$$F$$

$$2F$$

Solution

Question 9

$$1/4$$ times

$$4$$ times

$$1/2$$ times

unchanged

Solution

Question 10

$$ kg-f $$

$$ kg $$

$$ g $$

$$ m s^{-1} $$

Solution

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