Gravitation Test

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Gravitation Test - 46

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Weekly Quiz Competition

Question 1
1 / -0

Where is the intensity of the gravitational field of the earth maximum?

A
Centre of earth

B
Equator

C
Poles

D
Same everywhere

Solution

The earth is not a perfect sphere. As the radius of the earth increases from the poles to the equator, the value of $$g$$ becomes greater at the poles than at the equator.
Question 2
1 / -0

The value of 'g' at moon is $$\left ( \dfrac {1}{6} \right )^{th}$$ of that on earth. A balloon filled with hydrogen will :

A
fall with acceleration $$g$$ on the moon

B
rise with acceleration $$g$$ on the moon

C
rise with acceleration $$\dfrac{g}{6}$$ on the moon

D
fall with acceleration $$\dfrac{g}{6}$$ on the moon

Solution

Force on the balloon on moon $$F = Mg_{1}$$ ($$g_{1}$$ be the acceleration due to gravity on the surface of moon)

Hence, acceleration of balloon$$g_1 = \dfrac{F}{M}$$
Given that, $$g_{1}=\dfrac{g}{6}$$

Since the moon has no atmosphere, so there will not be air resistance.

Therefore it will fall down with acceleration $$\dfrac{g}{6}$$
Question 3
1 / -0

SI unit of G is $$Nm^{ 2 }{ kg }^{ -2 }$$. Which of the following can also be used as the SI unit of G?

A
$$ m^{ 3 }{ kg }^{ -1 }{ s }^{ -2 }$$

B
$$ m^{ 2 }{ kg }^{ -2 }{ s }^{ -1 }$$

C
$$ m { kg }^{ -3 }{ s }^{ -1 }$$

D
$$ m^{ 2 }{ kg }^{ -3 }{ s }^{ -2 }$$

Solution

Unit of $$G$$ is $$Nm^2kg^{-2}$$ as $$1N=kgms^{-2}$$.
So $$G$$ can be written as
$$kgms^{-2}\times m^2kg^{-2}=m^3kg^{-1}s^{-2}$$
Question 4
1 / -0

If mass of a body on the moon be denoted by $${ M }_{ m }$$ and on the earth be denoted by $$M_e$$, then

A
$${ M }_{ m }=\dfrac { 1 }{ 6 } M_e$$

B
$${ M}_{ m }={ M }_{ e }$$

C
$$M_{ m }=\sqrt { { M }_{ e } } $$

D
$${ M}_{ m }={ 6M }_{ e }$$

Solution

Mass of a body is constant that neither depends on the location of the body nor on the gravitational force exerted on the body.
So mass of the body will remain unchanged on moon i.e. $$M_m=M_e$$

Hence, correct answer is option $$B.$$
Question 5
1 / -0

A force of 50N is applied on a nail of area 0.001sq.cm. Then the thrust is:

A
50N

B
100N

C
0.05N

D
10N

Solution

Thrust is defined as the force applied on a small area resulting in high pressure hence according to question
Thrust = 50N.
Question 6
1 / -0

If a rock is brought from the surface of the moon,

A
its mass will change

B
its weight will change not mass

C
both mass and weight will change

D
its mass and weight both will remain same

Solution

Mass will remain same, but weight $$W=mg $$, As the rock is brought from moon , the gravity will change so the weight will also change.
Question 7
1 / -0

SI unit of G is.

A
$$N^2 -m^2/kg$$

B
$$N -m^2/kg$$

C
$$N -m/kg$$

D
$$N -m^2/kg^2$$

Solution

Hint: using the formula of gravitional constant
Step1:We know that
$$\mathrm{F}=\mathrm{G} \times \dfrac{M_{1} M_{2}}{r^{2}} \\$$
$$\mathrm{~F} \times \mathrm{r}^{2}=\mathrm{G} \times \mathrm{M}_{1} \mathrm{M}_{2} \\$$
$$\mathrm{~F} \times \dfrac{r^{2}}{M_{1} M_{2}}=\mathrm{G} \\$$
$$\mathrm{G}=\mathrm{F} \times \dfrac{r^{2}}{M_{1} M_{2}}$$
SI Unit of
$$\text { Force }=\mathrm{F}=\text { Newton } \\$$
$$\text { Distance }=\mathrm{R}=\mathrm{m} \\$$
$$\text { Mass }=\mathrm{M}=\mathrm{kg}$$
Step2: Now,
$$\mathrm{G}=\mathrm{F} \times \dfrac{r^{2}}{M_{1} M_{2}}$$
$$\mathrm{G}=\dfrac{\text { Newton } \times \text { Meter }^{2}}{\text { Kilogram } \times \text { Kilogram }}$$
$$\mathrm{G}=\dfrac{\text { Newton Meter }^{2}}{\text { Kilogram }^{2}}$$
$$\mathrm{G}=\mathrm{Nm}^{2} / \mathrm{kg}^{2}$$
So, SI Unit of $$\mathrm{G}$$ is $$\mathrm{Nm}^{2} / \mathrm{kg}^{2}$$

$$\textbf{Thus, option (D) is correct.}$$
Question 8
1 / -0

On the surface of the earth, force of gravitational attraction between two masses kept at distance $$d$$ apart is $$6 \ Newtons$$. If these two masses are taken to the surface of the moon and kept at the same distance $$d,$$ the force between them will be:

A
1N

B
36N

C
$$\frac { 1 }{ 6 } $$N

D
6N

Solution

By Universal law of gravitation, force of gravitational attraction between two masses kept at distance $$d$$ apart is
$$F_g=G\dfrac{m_1m_2}{d^2}=6 \ N$$

Gravitational force according to this law must remain the same even on the moon's surface, because none of the parameters $$m_1, m_2$$ and $$d$$ are changed. Since $$G$$ is universal gravitation constant. So $$G$$ is also constant, as the name suggest.

So, the force of gravitational attraction between them on moon's surface is still $$6 \ N.$$

Hence, $$(D)$$ is correct.
Question 9
1 / -0

The value of g near the earth's surface is.

A
$$8.9\ ms^{-2}$$

B
$$8.9\ ms^{-1}$$

C
$$9.8\ ms^{-2}$$

D
$$9.8\ ms^{-1}$$

Solution

Its value is $$9.8\ ms^{-2}$$ on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is $$9.8\ ms^{-2}$$. When discussing the acceleration of gravity, it was mentioned that the value of $$g$$ is dependent upon location.
Question 10
1 / -0

If the density of a metal is $$8.2 {g}/{cc}$$, its relative density is

A
$$8.2$$

B
$$\displaystyle\frac{1}{8.2}$$

C
$$0.82$$

D
None of these

Solution

Relative density is the ratio of density of substance to density of water
Density of substance=$$8.2gcm^{-3}$$ Density of water =$$1gcm^{-3}$$
Hence Relative density=$$\frac{8.2}{1}$$=$$8.2$$

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Gravitation Test - 46

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Gravitation Test - 46

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Question 1

Centre of earth

Equator

Poles

Same everywhere

Solution

Question 2

fall with acceleration $$g$$ on the moon

rise with acceleration $$g$$ on the moon

rise with acceleration $$\dfrac{g}{6}$$ on the moon

fall with acceleration $$\dfrac{g}{6}$$ on the moon

Solution

Question 3

$$ m^{ 3 }{ kg }^{ -1 }{ s }^{ -2 }$$

$$ m^{ 2 }{ kg }^{ -2 }{ s }^{ -1 }$$

$$ m { kg }^{ -3 }{ s }^{ -1 }$$

$$ m^{ 2 }{ kg }^{ -3 }{ s }^{ -2 }$$

Solution

Question 4

$${ M }_{ m }=\dfrac { 1 }{ 6 } M_e$$

$${ M}_{ m }={ M }_{ e }$$

$$M_{ m }=\sqrt { { M }_{ e } } $$

$${ M}_{ m }={ 6M }_{ e }$$

Solution

Question 5

50N

100N

0.05N

10N

Solution

Question 6

its mass will change

its weight will change not mass

both mass and weight will change

its mass and weight both will remain same

Solution

Question 7

$$N^2 -m^2/kg$$

$$N -m^2/kg$$

$$N -m/kg$$

$$N -m^2/kg^2$$

Solution

Question 8

1N

36N

$$\frac { 1 }{ 6 } $$N

6N

Solution

Question 9

$$8.9\ ms^{-2}$$

$$8.9\ ms^{-1}$$

$$9.8\ ms^{-2}$$

$$9.8\ ms^{-1}$$

Solution

Question 10

$$8.2$$

$$\displaystyle\frac{1}{8.2}$$

$$0.82$$

None of these

Solution

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