Gravitation Test

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Gravitation Test - 35

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Weekly Quiz Competition

Question 1
1 / -0

The ratio of the value of gravitational constant $$G$$ between Earth and Moon system and Earth and Sun system is:

A
Greater than $$1$$

B
Less than $$1$$

C
Equal to $$1$$

D
Can't be determined

Solution

According to Newton's law of gravitation, every body in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
$$F=\propto \dfrac{Mm}{r^2}$$

$$F=G \dfrac{Mm}{r^2}$$
Gravitational constant $$G$$ is the proportionality constant which has fixed value $$6.67408 × 10^{-11} m^3 kg^{-1} s^{-2}$$.
Therefore, the ratio of the value of gravitational constant $$G$$ between Earth and Moon system and Earth and Sun system is equal to 1. (Because it has the same value)
Question 2
1 / -0

Unit of acceleration due to gravity is:

A
$$ms^{-1}$$

B
$$ms^{-2}$$

C
$$ms^{-3}$$

D
$$ms^{-4}$$

Solution

Acceleration due to gravity is the acceleration of a body due the gravitational force.
$$F=mg$$
$$g=\frac{F}{m}$$
$$SI$$ units of acceleration due to gravity is $$ms^{-2}$$
Question 3
1 / -0

A satellite is moving around the Earth in a circular orbit with a velocity $$V$$. If the gravitational force of the Earth were to suddenly disappear, then the satellite would

A
fall towards the surface of the Earth.

B
spirally move away from the Earth.

C
move with a velocity $$V$$, tangentially to its circular orbit.

D
move radially outwards with a velocity $$V$$

Solution

The satellite is held in orbit because of two forces : gravitational force and centrifugal force. When the gravitational force disappears, there is no force to hold it in orbit. So it moves in the direction of its velocity, which is tangential to the circular path it was following earlier.
Question 4
1 / -0

Buoyant force acting on an object is equal to the ___

A
Mass of the solid

B
Weight of the solid

C
Weight of the liquid displaced by the object

D
Mass of the liquid displaced by the object.

Solution

Buoyant force acting on an object is equal to weight of liquid displaced by the solid i.e.
Buoyant force $$F_B$$:
$$ F_B = { V }_{ dis}\times { \rho }_{ l }\times g$$
here $${ V }_{ dis }$$ is the volume of displaced water.
$${ \rho }_{ l }$$ is density of liquid
$$g$$ is acceleration due to gravity.
Question 5
1 / -0

Let M denotes the mass of earth and let R denotes its radius. The ratio g/G at earth's surface is?

A
$$R^2/M$$

B
$$M/R^2$$

C
M/R

D
R/M

Solution

Gravity at the surface of earth $$g=\displaystyle\frac{GM}{R^2}$$
$$\displaystyle\frac{g}{G}=\frac{M}{R^2}$$.
Question 6
1 / -0

Why does a ship made of steel float on water while an oil-pin of steel sinks down?

A
Density of sea water is greater and hence the ship floats

B
Owing to the large volume of ship, it displaces more water, so up-thrust is more

C
The ship contains large air pockets which help it to float smoothly

D
In case of pin, the pressure is more since the area of its tip is small, so it sinks, but for ship the area of its base is more

Solution
Question 7
1 / -0

What will be the weight of a person on earth, who weights 9N on the moon?

A
$$3 N$$

B
$$15 N$$

C
$$45 N$$

D
$$54 N$$

Solution
Question 8
1 / -0

Gravitation on moon is $$\dfrac{1}{6}$$th of that on earth . When a balloon filled with hydrogen is released on moon then this:

A
will rise with an acceleration less then $$\dfrac{g}{6}$$

B
will rise with acceleration $$\dfrac{g}{6}$$

C
will fall down with an acceleration less then $$\dfrac{5g}{6}$$

D
will fall down acceleration $$\dfrac{g}{6}$$

Solution

There is no atmosphere on the moon. On earth, air provides enough Buoyant Force. So,that the balloon rises up. Thus, on moon, only gravity acts on it and so it will fall down with acceleration $$= \dfrac{g}{6}$$
Question 9
1 / -0

A body is brought from the earth to the moon is ___

A
Mass will change

B
Weight will change

C
Mass and weight will change

D
Both mass and weight will change

Solution

When we leave the surface of the earth our body weight decreases, mass remains the same, this is due to the gravitational pull on the moon. The gravitational pull is less on the moon than the earth, hence the weight is less. The size of the moon is smaller, only one six of the earth, that is why our weight on the moon is less
Question 10
1 / -0

How much will a person with 72 N weight on Earth,weight on the moon?

A
12 N

B
36 N

C
21 N

D
63 N

Solution

We know,

$$ g_{earth} = \dfrac{GM}{R^{2}} $$ where, M = mass of planet (earth)

As moon is lighter than the earth i.e, approx
mass of moon $$ = \dfrac{1}{6} $$ (mass of earth)

$$ \Rightarrow g_{moon} = \dfrac{GM}{R^{2}6} = \dfrac{g_{earth}}{6} $$

Thus, weight of man on moon is

$$ = mg_{moon} = \dfrac{mg_{earth}}{6} = \dfrac{72}{6} = 12 N $$

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Re-Attempt Weekly Quiz Competition

Gravitation Test - 35

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Gravitation Test - 35

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SHARING IS CARING

Question 1

Greater than $$1$$

Less than $$1$$

Equal to $$1$$

Can't be determined

Solution

Question 2

$$ms^{-1}$$

$$ms^{-2}$$

$$ms^{-3}$$

$$ms^{-4}$$

Solution

Question 3

fall towards the surface of the Earth.

spirally move away from the Earth.

move with a velocity $$V$$, tangentially to its circular orbit.

move radially outwards with a velocity $$V$$

Solution

Question 4

Mass of the solid

Weight of the solid

Weight of the liquid displaced by the object

Mass of the liquid displaced by the object.

Solution

Question 5

$$R^2/M$$

$$M/R^2$$

M/R

R/M

Solution

Question 6

Density of sea water is greater and hence the ship floats

Owing to the large volume of ship, it displaces more water, so up-thrust is more

The ship contains large air pockets which help it to float smoothly

In case of pin, the pressure is more since the area of its tip is small, so it sinks, but for ship the area of its base is more

Solution

Question 7

$$3 N$$

$$15 N$$

$$45 N$$

$$54 N$$

Solution

Question 8

will rise with an acceleration less then $$\dfrac{g}{6}$$

will rise with acceleration $$\dfrac{g}{6}$$

will fall down with an acceleration less then $$\dfrac{5g}{6}$$

will fall down acceleration $$\dfrac{g}{6}$$

Solution

Question 9

Mass will change

Weight will change

Mass and weight will change

Both mass and weight will change

Solution

Question 10

12 N

36 N

21 N

63 N

Solution

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