Gravitation Test

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Gravitation Test - 41

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Question 1
1 / -0

Fill in the blank.
The loss of weight of an object that is immersed in water is numerically equal to the ________ .

A
buoyant force

B
density of the body

C
volume of the body

D
volume of the liquid

Solution

Buoyant Force. When a rigid object is submerged in a fluid (completely or partially), there exits an upward force on the object that is equal to the weight of the fluid that is displaced by the object.
When the object is removed, the volume that the object occupied will fill with fluid. This volume of fluid must be supported by the pressure of the surrounding liquid since a fluid can not support itself. When no object is present, the net upward force on this volume of fluid must equal to its weight, i.e. the weight of the fluid displaced. When the object is present, this same upward force will act on the object.
Question 2
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As per the request of one of his friends from equator, Rahul buys 100 gram of silver at the north pole. He hands it over to his friend at the equator. The weight found by friend will be __________ the weight of silver bought.

A
greater than

B
less than

C
same as

D
can't say

Solution

Rahul's friend, at the equator, will receive 100 gram of silver. But the weight of the same will be less than that measured by Rahul at the north pole. This is because the value of 'g' is less in equator than the poles.
Question 3
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If the acceleration due to gravity on the surface of the earth is $$9.8\,\,m/s^2$$, what will be the acceleration due to gravity on the surface of a planet whose mass and radius both are two times the corresponding quantities for the earth ?

A
$$4.9\,\,m/s^2$$

B
$$9.8\,\,m/s^2$$

C
$$19.8\,\,m/s^2$$

D
None of the above

Solution

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

So, $$g_p = (\dfrac{M_p}{ M_e} \times (\dfrac{R_e} {R_p})^2) g $$
$$ = 2 \times (\dfrac{1}{2})^2 g $$
$$ = \dfrac{g}{2} = 4.9\ m/ s^2 $$
Question 4
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If the weight of a body on the surface of the moon is 100 N, what is its mass? (g =1.6 m$$s^{-2}$$)

A
160 kg

B
62.5 kg

C
6.25 kg

D
625 kg

Solution

$$ m= W/g_m $$
$$ m= 100/1.6 $$
$$ m= 62.5 kg$$
Question 5
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Calculate the force of gravitation between the earth and the sun, given that the mass of the earth is $${6\times 10^{24}}\ kg$$ and the sun is $${2\times 10^{30}}\ kg$$. The average distance between the two is $${1.5\times 10^{11}}\ m$$.

A
$${35.57\times 10^{21}\ N}$$

B
$${35.57\times 10^{20}\ N}$$

C
$${35.57\times 10^{19}\ N}$$

D
$${35.57\times 10^{22}\ N}$$

Solution

Given,
Mass of Earth, $$M_e=6\times10^{24}\ kg$$
Mass of sun, $$M_s=2\times10^{30}\ kg$$
Distance between the earth and sun, $$R= 1.5\times10^{11}\ m$$

According to Newton's law of gravitation,
$$F_g=\dfrac{GM_eM_s}{R^2}$$

$$F_g=\dfrac{6.67\times10^{-11}\times(6\times10^{24})\times(2\times10^{30})}{(1.5\times10^{11})^2}$$

$$F_g=35.57\times10^{21} N$$
Question 6
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Two fishes are $$1 m$$ apart underwater. The gravitational force between them is $${F_1}$$,They jump above the surface of water keeping the same distance (i.e $$1 m$$) between them. The new gravitational force between them is $${F_2}$$. The relationship between $${F_1}$$ and $${F_2}$$ is

A
$${F_1}$$> $${F_2}$$

B
$${F_1}$$< $${F_2}$$

C
$${F_1=F_2}$$

D
$${F_1:F_2}= 1:2$$

Solution

Answer is C.

The force of gravity between two objects is determined by the mass of each object and the distance between their centers. Objects with a greater amount of mass will exert a greater degree of gravitational pull, but as the distance between two objects increases, the gravitational force between them lessens.
In this case, the distance between the two fishes remains the same both inside and outside the water. So the force between them remains the same both inside and outside the water. That is, $${F_1=F_2}$$.
Question 7
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Observe the diagram and identify a liquid/liquids denser than water

A
Glycerin, Mercury, Oil

B
Glycerin, Mercury

C
Kerosene, Glucerin

D
Oil, Kerosene

Solution

A liquid that is denser than water will be lying below water when filled into the glass. So glycerine and mercury are denser than water.
Question 8
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_______ of a body changes from place to place but its ______ remains constant.

A
Weight, mass

B
Mass, weight

C
Mass, force

D
Mass, gravity

Solution

Mass is the amount of matter occupied by a body. It remains the same whether the object is on the earth, the moon or even in outer space.

On the other hand, the weight of a body is the force with which it is attracted towards the earth.

Mass $$m$$ is a constant quantity and weight $$W=mg.$$
Since acceleration due to gravity $$g$$ is different for different places, $$W$$ changes from place to place.
Question 9
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Gravitational force on the surface of the moon is only $${\frac{1}{6}}$$ as strong as gravitational force on the earth. What is the weight in Newton of a 10 kg object on the moon ?

A
16.66 N

B
15 N

C
17.53 N

D
16 N

Solution

W=mg
m= 10 kg, $$g_e=9.8 m/s^2$$
On earth, $$W=98 N$$
On moon, $$g_m=g_e/6$$
Hence, $$W_m=W_e/6=98/6=16.66 N$$
Question 10
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Is the buoyant force on a submerged object equal to the weight of the object itself or equal to the weight of the fluid displaced by the object?

A
Equal to the weight of the object itself

B
Equal to the weight of the fluid displaced by the object

C
A and B as both are same

D
None of the above

Solution

According to $$Archimedes' \ principle$$, any body completely or partially submerged in a fluid at rest is acted upon by an upward or buoyant force whose magnitude is equal to the weight of the fluid displaced by the body.

$$\therefore$$ Loss in weight of body = Weight of water (liquid) displaced by the body = Buoyant force or upthrust exerted by water (any liquid) on the body.
Hence, the buoyant force on a submerged object equal to the weight of the fluid displaced by the object.

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Gravitation Test - 41

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Gravitation Test - 41

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Question 1

buoyant force

density of the body

volume of the body

volume of the liquid

Solution

Question 2

greater than

less than

same as

can't say

Solution

Question 3

$$4.9\,\,m/s^2$$

$$9.8\,\,m/s^2$$

$$19.8\,\,m/s^2$$

None of the above

Solution

Question 4

160 kg

62.5 kg

6.25 kg

625 kg

Solution

Question 5

$${35.57\times 10^{21}\ N}$$

$${35.57\times 10^{20}\ N}$$

$${35.57\times 10^{19}\ N}$$

$${35.57\times 10^{22}\ N}$$

Solution

Question 6

$${F_1}$$> $${F_2}$$

$${F_1}$$< $${F_2}$$

$${F_1=F_2}$$

$${F_1:F_2}= 1:2$$

Solution

Question 7

Glycerin, Mercury, Oil

Glycerin, Mercury

Kerosene, Glucerin

Oil, Kerosene

Solution

Question 8

Weight, mass

Mass, weight

Mass, force

Mass, gravity

Solution

Question 9

16.66 N

15 N

17.53 N

16 N

Solution

Question 10

Equal to the weight of the object itself

Equal to the weight of the fluid displaced by the object

A and B as both are same

None of the above

Solution

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