Gravitation Test

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Gravitation Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

The value of g on the surface of moon is:

A
zero

B
the same as on the surface of the earth

C
more than that on the surface of the earth

D
less than that on the surface of the earth

Solution

Answer is D.

Because the moon has less mass than Earth, the force due to gravity at the lunar surface is only about 1/6 of that on Earth.
Hence, the value of g on the surface of moon is less than that on the surface of the earth.
Question 2
1 / -0

Specific gravity of substance is

A
Density of substance relative to density of air

B
Density of substance relative to density of water

C
Density of substance relative to density of hydrogen

D
none of these

Solution

Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest; for gases, the reference is air at room temperature.
$$\text{ specific density } = \dfrac{ \text{ density of unknown material } }{ \text{ density of water } }$$
Question 3
1 / -0

The gravitational force between two stones of mass $$1\ kg$$ each, separated by a distance of $$1\ m$$ in a vacuum is ($$ G= 6.674\times 10^{-11} N m^2/ kg^2$$)

A
Zero

B
$$6.674\times 10^{-5}N$$

C
$$6.674\times 10^{-8}N$$

D
$$6.674\times 10^{-11}N$$

Solution

Using universal law of gravitation,
$$F=\cfrac{GmM}{R^2}$$
Distance between two stones, $$R= 1\ m$$
Mass of both the stones, $$m=M= 1\ kg$$
$$F= \cfrac{G(1\ kg)(1\ kg)}{(1\ m)^2}$$
$$F= 6.674\times 10^{-11} N$$
Question 4
1 / -0

The value of G does not depend on

A
nature of the interacting bodies

B
size of the interacting bodies

C
mass of the interacting bodies

D
all the above

Solution

G or the Universal gravitational constant remains constant throughout the universe and its value is $$6.67 \times 10^{-11} m^3kg^{-1} s^{-2}$$. It is not affected by any factor.
$$F = \dfrac{GmM}{r^2} \ \Rightarrow F \propto \dfrac{Mm}{r^2}$$
G is a proportionality constant and is independent of all variables.
Question 5
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If the distance between two masses be doubled, then the force between will become

A
$$1/4\:times$$

B
$$4 times$$

C
$$1/2\:times$$

D
$$2 times$$

Solution

Answer is A.

The gravitational force between two objects is inversely proportional to the square of distance between them.
So, if the distance between two objects is doubled, then the gravitational force becomes $$\cfrac { 1 }{ 2\times 2 } $$.
That is, $$1/4. $$
Therefore, if the distance between two masses be doubled, then the force between will becomes 1/4.
Question 6
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The weight of a body is $$120 N$$ on the earth. If it is taken to the moon, its weight and mass will be about (Take g$$_e$$ = 10 m/s$$^2$$)

A
$$120 N, 120 kg$$

B
$$60 N, 12 kg$$

C
$$20 N, 12 kg$$

D
$$720 N, 120 kg$$

Solution

It is given that the weight of the object on the earth is $$120 N$$. That is $$W(e) = 120 N$$. Acceleration due to gravity is $$10 m/s.$$
Mass of the object on earth, m(e) is calculated as follows.
We know, $$W(e) = M(e) \times g$$
Therefore, $$120 N = M(e) \times 10$$. That is, $$M(e) = 120/10 = 12 kg$$
Thus, the massof the object on earth is $$12 kg$$. We know that the mass of the object remains the same through out the universe. Hence, mass of the object on the moon is also $$12 kg$$.
We know, weight of the object on the moon $$= 1/6$$ of the weight of the object on the earth.
Therefore, $$W(m) = 1/6 \times W(e)$$
That is, $$W(m) = 1/6 \times 120 N = 20 N$$
Hence, the weight and mass of the object on the moon are $$20 N$$ and $$12 kg$$ respectively.
Question 7
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The acceleration due to gravity on the moon is one-sixth that on the earth. A high jumper can jump $$2m$$ on earth. What distance can he jump on the moon?

A
$$2\ m$$

B
$$6\ m$$

C
$$12\ m$$

D
$$18\ m$$

Solution

Let $$W_o$$ & $$W_n$$ are the weight of a body on the earth and the moon respectively.
$$h_e$$ and $$h_m$$ are the height of the jumper achieved respectively
Energy in both cases will be the same.
So that $$w_eh_e = W_mh_m$$
or $$h_m=\dfrac {w_eh_e}{W_m}$$
$$ h_m=\dfrac {w_eh_e}{w_e/6}$$
$$\Rightarrow h_m = 6 \times h_0$$
$$\Rightarrow h_m = 6 \times 2$$
$$\Rightarrow h_m = 12 m$$
Question 8
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The weight of a boy on the surface of the moon is $$300\ N$$. The weight of this boy on the surface of the earth is:

A
$$300\ N$$

B
$$5\ N$$

C
$$50\ N$$

D
$$1800\ N$$

Solution

Weight of the boy on the surface of the moon = $$300 N$$
The value of acceleration due to gravity on the moon is 1/6th of the value of $$g$$ on the earth.
Weight of the boy on the surface of the earth = $$300 \times 6 = 1800\ N$$
Question 9
1 / -0

An object weighs $$W\ N$$ when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?

A
$$\dfrac{W}{6}\ N$$

B
$$6W\ N$$

C
$$W\ N$$

D
$$Zero$$

Solution

Given,
Weight of an object on the surface of the earth $$=W\ N$$
Weight of object on the moon $$=\dfrac 16 \times $$ its weight on the earth

Weight of object on the moon $$=\dfrac 16 \times W$$

Weight of object on the moon $$=\dfrac W6 \ N$$
Question 10
1 / -0

The force of gravitation between two bodies does not depend upon

A
the separation between them

B
the gravitational constant

C
the product of their masses

D
the sum of their masses

Solution

The force of gravitation between the two bodies $$=\dfrac{GMm}{r^2} $$

Where G is gravitational constant

r is separation between the two bodies

M is mass of one body

m is mass of the other body

From the above expression we can easily see that the force doesn't depend on the sum of the masses of the bodies

Hence correct answer is option $$D$$

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Gravitation Test - 23

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Gravitation Test - 23

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Question 1

zero

the same as on the surface of the earth

more than that on the surface of the earth

less than that on the surface of the earth

Solution

Question 2

Density of substance relative to density of air

Density of substance relative to density of water

Density of substance relative to density of hydrogen

none of these

Solution

Question 3

Zero

$$6.674\times 10^{-5}N$$

$$6.674\times 10^{-8}N$$

$$6.674\times 10^{-11}N$$

Solution

Question 4

nature of the interacting bodies

size of the interacting bodies

mass of the interacting bodies

all the above

Solution

Question 5

$$1/4\:times$$

$$4 times$$

$$1/2\:times$$

$$2 times$$

Solution

Question 6

$$120 N, 120 kg$$

$$60 N, 12 kg$$

$$20 N, 12 kg$$

$$720 N, 120 kg$$

Solution

Question 7

$$2\ m$$

$$6\ m$$

$$12\ m$$

$$18\ m$$

Solution

Question 8

$$300\ N$$

$$5\ N$$

$$50\ N$$

$$1800\ N$$

Solution

Question 9

$$\dfrac{W}{6}\ N$$

$$6W\ N$$

$$W\ N$$

$$Zero$$

Solution

Question 10

the separation between them

the gravitational constant

the product of their masses

the sum of their masses

Solution

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