Gravitation Test

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Gravitation Test - 40

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Weekly Quiz Competition

Question 1
1 / -0

A man weighs $$600\ N$$ on earth. What would be his approximate weight on moon?

A
$$100$$ $$N$$

B
$$200$$ $$N$$

C
$$50$$ $$N$$

D
$$600$$ $$N$$

Solution

Weight on earth = $$600 N$$
Let $$g =$$ $$10 m/s^{2} $$ on earth
Mass on earth = $$\dfrac{600}{10} = 60\ kg$$
Now, since mass is a constant quantity so, it will remain $$ 60\ kg$$ on the moon also.
Now, weight on moon = $$mg'$$
$$m =$$ mass $$ =60\ kg$$
$$g'$$ = acc. due to gravity on moon = $$\dfrac{1}{6}^{th}$$ the value on earth
So, Weight on moon = $$\dfrac{1}{6}^{th}$$ of the weight on earth

$$\Rightarrow$$ Weight on the moon $$= 600\times \dfrac{1}{6} = 100\ N $$
Question 2
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The force of attraction between two bodies at a certain separation is $$10 N$$. What will be the force of attraction between them if the separation between them is reduced to half?

A
$$2.5$$ $$N$$

B
$$5$$ $$N$$

C
$$20$$ $$N$$

D
$$40$$ $$N$$

Solution
Question 3
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A man first swims in sea water and then in river water. Compare the weights of sea water and river water displaced by him.

A
Weight of sea water > Weight  of river water

B
Weight  of sea water = Weight  of river water

C
Weight  of sea water < Weight  of river water

D
None of the above

Solution

$$1:1$$ (in each case the weight of water displaced will be equal to the weight of man).
According to Archimedes Principle the volume of water displaced is equal to the weight of the body.
Since, the weight in both the case is the same, so the weight of water displaced in sea water and in river water will also be same.
Question 4
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What force and weight act on a mass of $$10.5 kg$$ being pulled by earth? Take $$g=10 m {s}^{-2}$$.

A
105 N, 10.5 N

B
105 N, 105 N

C
100 N, 105 N

D
10.5 N, 10.5 N

Solution

$$Force = mg$$
$$\Rightarrow F = 10.5 \times 10 =105 N$$

$$Weight = mg$$
$$\Rightarrow W = 10.5\times10 =105 N$$
Question 5
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An artificial satellite orbiting the earth does not fall down because of the earth's attraction

A
Is balanced by the attraction of the moon

B
Vanishes at such distances

C
Is balanced by the viscous drag produced by the atmosphere

D
Produces the necessary accelaration of its motion in a curved path

Solution

We observe weightlessness in satellite because the net magnitude of force on the body is almost zero i.e. earth's gravitation is nullified in terms of magnitude by centrifugal force. But, earth's gravitation is necessary to change the direction of satellite continously and thus providing the acceleration in terms of change in direction.
Question 6
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The weight of a body on earth is $$98 N$$ where acceleration due to gravity is $$9.8 \ m {s}^{-2}$$. What will be its weight on the moon where acceleration due to gravity is $$1.6 \ m {s}^{-2}$$?

A
$$10\ kg$$

B
$$10 \ N$$

C
$$16\ kg$$

D
$$16 \ N$$

Solution

Weight on Earth ,$$W_e = 98\ N = mg$$
$$m = \dfrac{W_e}{g_e} = \dfrac{98}{9.8} = 10 \ kg$$

$$m= 10\ kg , g = 1.6\ m/s^{2} $$
So, weight on Moon, $$ W_m= mg_m$$
$$W_m = 10\times 1.6 =16 \ N$$
Question 7
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The ratio: $$\dfrac{g_{Earth}}{g_{Moon}}$$ is equal to:

A
$$6$$

B
$$\dfrac{1}{10}$$

C
$$\dfrac{1}{2}$$

D
none of the above

Solution

Answer is A.

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.
$$g_{Earth} = 9.81\ m/{ s }^{ 2 }$$
$$g_{Moon} = 1.625\ m/{ s }^{ 2 }$$.
So, the ratio:
$$\dfrac{g_{Earth}}{g_{Moon}}=\dfrac{9.81}{1.625} = 6$$

Hence earth has 6 time of moon's gravity.
Question 8
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A rectangular box is kept over a table with different faces touching the table. In different cases, the block exerts

A
same thrust and same pressure

B
same thrust and different pressure

C
different thrust and same pressure

D
different thrust and different pressure

Solution

Answer is B.

In all the cases the block exerts the same force on the ground. But the force in position when the rectangular block rests along its length, it is spread over a large area, so the force on each square meter is reduced. The pressure under this position is less than that under position when the rectangular block rests along its breadth.
From, this we infer that when the area is very much smaller, the pressure is very much greater and vice-versa.
Hence, in this case, the block exerts same thrust or force on all the sides and different pressures on the length and breadth sides.
Question 9
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Ships and submarines works on the principle/law of

A
Newton law of motion

B
Archimedes principle

C
Bernoulli's principle

D
None of the above

Solution

Archimedes' principle states that the upward buoyant force acting on the body is equal to the weight of the fluid it displaces. It has the following applications-

Submarine:
A submarine has a large ballast tank, which is used to control its position and depth from the surface of the sea. A submarine submerges by letting water into the ballast tank so that its weight becomes greater than the buoyant force. Conversely, it floats by reducing water in the ballast tank.-thus its weight is less than the buoyant force.
Question 10
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If $$M$$ is the mass of the earth and $$R$$ its radius, the ratio of the gravitational acceleration and the gravitational constant is:

A
$$\displaystyle\frac{R^{2}}{M}$$

B
$$\displaystyle\frac{M}{R^{2}}$$

C
$$MR^{2}$$

D
$$\displaystyle\frac{M}{R}$$

Solution

Let us consider a body of mass m on surface of earth.
Gravitational force on it $$F=mg$$
By Newton's law of gravitation $$F$$ is also $$G \dfrac{Mm}{R^2}$$
So $$mg=G\dfrac{Mm}{R^{2}}$$
$$\therefore$$ On rearranging, $$\displaystyle\frac{g}{G}=\displaystyle\frac{M}{R^{2}}$$

Thus, option B is correct.

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Gravitation Test - 40

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Gravitation Test - 40

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Question 1

$$100$$ $$N$$

$$200$$ $$N$$

$$50$$ $$N$$

$$600$$ $$N$$

Solution

Question 2

$$2.5$$ $$N$$

$$5$$ $$N$$

$$20$$ $$N$$

$$40$$ $$N$$

Solution

Question 3

Weight of sea water > Weight of river water

Weight of sea water = Weight of river water

Weight of sea water < Weight of river water

None of the above

Solution

Question 4

105 N, 10.5 N

105 N, 105 N

100 N, 105 N

10.5 N, 10.5 N

Solution

Question 5

Is balanced by the attraction of the moon

Vanishes at such distances

Is balanced by the viscous drag produced by the atmosphere

Produces the necessary accelaration of its motion in a curved path

Solution

Question 6

$$10\ kg$$

$$10 \ N$$

$$16\ kg$$

$$16 \ N$$

Solution

Question 7

$$6$$

$$\dfrac{1}{10}$$

$$\dfrac{1}{2}$$

none of the above

Solution

Question 8

same thrust and same pressure

same thrust and different pressure

different thrust and same pressure

different thrust and different pressure

Solution

Question 9

Newton law of motion

Archimedes principle

Bernoulli's principle

None of the above

Solution

Question 10

$$\displaystyle\frac{R^{2}}{M}$$

$$\displaystyle\frac{M}{R^{2}}$$

$$MR^{2}$$

$$\displaystyle\frac{M}{R}$$

Solution

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