Gravitation Test

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Gravitation Test - 33

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Question 1
1 / -0

Which Newton's laws describe thrust?

A
First and Second

B
Second and Third

C
Only Second

D
First and Third

Solution

Thrust is a reaction force described quantitatively by Newton's second and third laws. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction on that system.
Question 2
1 / -0

Two block of mass $$m_1$$ and $$m_2$$ are kept $$d$$ apart from each other. What happens to the magnitude of the gravitational force $$F$$ acting on the two blocks, if the distance between the center of the masses is halved?

A
It is quadrupled

B
It is doubled

C
It remain the same

D
It is halved

E
It is quartered

Solution

Distance between the masses initially is $$d$$.

Gravitational force acting between two blocks of mass $$m_1$$ and $$m_2$$ is given by
$$F = \dfrac{Gm_1 m_2}{d^2}$$
Now the distance between them is halved keeping all the parameters same i.e $$d' = d/2$$

Thus gravitational force $$F' = \dfrac{Gm_1 m_2}{(d/2)^2} =4F$$

Thus the force is quadrupled.
Question 3
1 / -0

Which of the following equations or principle is most suitable to solve given question.
The distance between two small sphere is $$d$$ and mass of each sphere is $$ m$$. What force do they apply to each other?

A
Newton's first law ( law of inertia)

B
Newton's second law ($$F_{net}$$ = ma)

C
Newton's third law (For every action there is an equal and opposite reaction)

D
Newton's law of universal gravitation

E
Conservation of linear momentum

Solution

Newton's law of gravitation quantifies the force of attraction between two masses $$m_1,m_2$$ separated by a distance $$d$$ as $$F=\dfrac{Gm_1m_2}{d^2}$$
Thus the force the spheres apply to each other, according to Newton's Law of Gravitation $$=\dfrac{Gm^2}{d^2}$$
Question 4
1 / -0

Two block of mass $$m_1$$ and $$m_2$$ are kept apart d from each other. What happen to the magnitude of the force on $$ m_{1}$$ if the mass of $$m_{2}$$ is doubled?

A
It is quadrupled

B
It is doubled

C
It remain the same

D
It is halved

E
It is quartered

Solution

Initial force on $$m_1$$ due to $$m_2$$, $$F = \dfrac{Gm_1 m_2}{d^2}$$
Now the mass of $$m_2$$ is doubled keeping all the parameters same i.e $$m'_2 = 2m_2$$
Thus new force on $$m_1$$ $$F' = \dfrac{Gm_1 (2m_2)}{d^2} =2F$$
Thus the force also gets doubled.
Question 5
1 / -0

We have a substance having density x kept in a medium of density y. Then what is its relative density with respect to the medium?

A
$$\dfrac{x}{y}$$

B
$$xy$$

C
$$xy^2$$

D
$$x^2y$$

Solution

Relative density is defined as the ratio of density of substance to the density of medium.
$$\therefore$$ Relative density $$r = \dfrac{x}{y}$$
Question 6
1 / -0

Relation between density ($$\rho$$), relative density $$r$$, and density of water $$\rho_o$$ is given by:

A
$$r=\dfrac{\rho}{\rho_o}$$

B
$$r=\dfrac{\rho_o}{\rho}$$

C
$$r=\rho \rho_o$$

D
$$r=\dfrac{\rho}{\rho_o^2}$$

Solution

Relative density is defined as the ratio of density of substance to the density of water.
$$\therefore$$ Relative density, $$r = \dfrac{\rho}{\rho_o}$$
Question 7
1 / -0

If we consider the gravitational force F between two objects of masses $$m_1$$ and $$m_2$$ respectively, separated by a distance R , and we double the distance between them, what is the new magnitude of the gravitational force between them?

A
F/4

B
F/2

C
F

D
2F

E
4F

Solution

According to Sir Newton's gravitational law the magnitude of gravitational force $$F$$ between objects of mass $$m_{1}$$ and $$m_{2}$$ separated by a distance $$R$$ is given by ,
$$F=G\dfrac{m_{1}m_{2}}{R^{2}}$$ ............$$eq1$$ ,
now if the distance between them is doubled i.e. $$2R$$ ,then the gravitational force will be ,
$$F'=G\dfrac{m_{1}m_{2}}{\left(2R\right)^{2}}=G\dfrac{m_{1}m_{2}}{4R^{2}}$$ ,
now by using $$eq1$$ ,
$$F'=F/4$$
Question 8
1 / -0

If volume of a steel ball is halved and its mass remains constant, its relative density will be:

A
same

B
doubled

C
halved

D
can't be determined

Solution

Relative density of steel ball is given by
$$r = \dfrac{\rho_s}{\rho_w} = \dfrac{m}{V\rho_w}$$

where, $$\rho_s$$ is the density of ball and $$\rho_w$$ is the density of water
$$\implies r \propto \dfrac{1}{V}$$ $$(\because m =constant)$$

Hence, relative density is inversely proportional to the volume of the ball.

Thus relative density is doubled when the volume of steel ball is halved.
Question 9
1 / -0

Assuming a person could survive in all of the following locations, where would this person have the most mass?

A
on the surface of the earth

B
on the surface of the moon

C
on the surface of Jupiter

D
on the surface of the sun

E
same mass at all locations

Solution

The weight ($$W=mg$$) of an object depends upon the gravitational acceleration (g). Since the value of $$g$$ is different at different places, the weight of the person will be different at different locations.
But, mass is the intrinsic property of the person. It does not change by changing the position. Hence, the mass of the person will be the same in all locations.
Question 10
1 / -0

A globe of steel has a mass of 12 g and a volume of $$15.2 cm^3$$. Find its relative density wrt water.

A
0.25

B
0.79

C
1.25

D
1.56

Solution

Density ($$\rho_s$$) = $$\dfrac{mass(m)}{volume(V)}$$
Relative density of steel with respect to water=$$\dfrac{\rho_s}{\rho_w}$$
$$=\dfrac{m/V}{\rho_{w}}$$
$$=\dfrac{12/15.2}{1}$$
$$=\dfrac{12}{15.2}$$
$$=0.79\ g/cm^3$$

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Gravitation Test - 33

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Gravitation Test - 33

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Question 1

First and Second

Second and Third

Only Second

First and Third

Solution

Question 2

It is quadrupled

It is doubled

It remain the same

It is halved

It is quartered

Solution

Question 3

Newton's first law ( law of inertia)

Newton's second law ($$F_{net}$$ = ma)

Newton's third law (For every action there is an equal and opposite reaction)

Newton's law of universal gravitation

Conservation of linear momentum

Solution

Question 4

It is quadrupled

It is doubled

It remain the same

It is halved

It is quartered

Solution

Question 5

$$\dfrac{x}{y}$$

$$xy$$

$$xy^2$$

$$x^2y$$

Solution

Question 6

$$r=\dfrac{\rho}{\rho_o}$$

$$r=\dfrac{\rho_o}{\rho}$$

$$r=\rho \rho_o$$

$$r=\dfrac{\rho}{\rho_o^2}$$

Solution

Question 7

F/4

F/2

F

2F

4F

Solution

Question 8

same

doubled

halved

can't be determined

Solution

Question 9

on the surface of the earth

on the surface of the moon

on the surface of Jupiter

on the surface of the sun

same mass at all locations

Solution

Question 10

0.25

0.79

1.25

1.56

Solution

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