Gravitation Test

Result

Gravitation Test - 64

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Weekly Quiz Competition

Question 1
1 / -0

If the ratio of the masses of two planets is $$8 : 3$$ and the ratio of their diameters is $$2 : 3$$, then what will be the ratio of their acceleration due to gravity?

A
$$ \dfrac {1}{6}$$.

B
$$ \dfrac {6}{1}$$.

C
$$ \dfrac {2}{3}$$.

D
$$ \dfrac {9}{1}$$.

Solution

We know that $$g=\dfrac { GM }{ { R }^{ 2 } } $$
Given that,
$$R_2:R_1=\dfrac { 3 }{ 2 } =1.5$$ and $$M_1:M_2=8:3$$
So,
$$\dfrac { { g }_{ 1 } }{ { g }_{ 2 } } =\dfrac { { GM }_{ 1 } }{ { R }_{ 1 }^{ 2 } } \div \dfrac { { GM }_{ 2 } }{ { R }_{ 2 }^{ 2 } } $$
$$\Rightarrow \dfrac { { g }_{ 1 } }{ { g }_{ 2 } } =\dfrac { { M }_{ 1 } }{ { M }_{ 2 } } \times \dfrac { { R }_{ 2 }^{ 2 } }{ { R }_{ 1 }^{ 2 } } $$
$$=\dfrac { 8 }{ 3 } \times { \left( \dfrac { \dfrac { 3 }{ 2 } }{ 1 } \right) }^{ 2 }$$
$$=\dfrac { 8 }{ 3 } \times \dfrac { 9 }{ 4 } $$
$$=6:1$$
Question 2
1 / -0

The density of ice, if density of water is $$1 g/cm^3$$ and relative density of ice is $$0.92$$, will be:

A
$$ 1 g/cm^3$$

B
$$ \dfrac{1}{0.92} g/cm^3$$

C
$$0.92 g/cm^3$$

D
None of these

Solution

we know that,

$$Relative$$ $$density$$ = $$\frac{Density \quad of\quad substance}{Density \quad of \quad water}$$
Density of water = $$1g/cm^3$$

$$0.92=\frac{Density(i c e)}{1}$$

Density $$(i c e)=0.92 g / c m^{3}$$

Answer:(c) $$0.92 \mathrm{~g} / \mathrm{cm}^{3}$$
Question 3
1 / -0

A ball is dropped from the top of building. The ball takes $$0.5s$$ to fall post the $$3m$$ length of window some distance from the top of the building. If the velocity of the ball at the top and at the bottom of the window are $$V_T$$ and $$V_B$$ respectively, then

A
$$V_T+V_B=12ms^{-1}$$

B
$$V_T+V_B=4.9ms^{-1}$$

C
$$V_B\times V_T=1ms^{-1}$$

D
$$\dfrac{V_B}{V_T}=1ms^{-1}$$
Question 4
1 / -0

A point P lies on the axis of a ring of mass M and radius a, at a distance a from its centre C. A small particle starts from P and reaches C under gravitational attraction only. Its speed at C will be

A
$$\sqrt{\dfrac{2GM}{a}}$$

B
$$\sqrt{\dfrac{2GM}{a}\left ( 1-\frac{1}{\sqrt{2}} \right )}$$

C
$$\sqrt{\dfrac{2GM}{a}\left ( \sqrt{2}-1 \right )}$$

D
Zero

Solution
Question 5
1 / -0

A body weight $$700 \ g-wt$$ on the earth. How much will it weigh will it weight on the surface of a planet whose mass is $$\dfrac{1}{7}$$th and radius is half that of the earth

A
$$200g\,wt$$

B
$$400g\,wt$$

C
$$50g \,wt$$

D
$$300g \,wt$$

Solution
Question 6
1 / -0

The maximum height from which a person can safely jump is 2.45 m. What is the maximum allowable landing speed for a parachutist?

A
5.93 $$m/s$$

B
6.93 $$m/s$$

C
4.93 $$m/s^2$$

D
69.3 $$m/s$$

Solution
Question 7
1 / -0

A body has a weight $$90\ N$$ on the earth's surface. The mass of the moon is $$\dfrac{1}{9}$$ that of the earth's mass and its radius is $$\dfrac{1}{2}$$ that of the earth's radius. On the moon, the weight of the body is :

A
$$45\ N$$

B
$$202.5\ N$$`

C
$$90\ N$$

D
$$40\ N$$
Question 8
1 / -0

Who among the following did first give the experimental value of $$G$$?

A
Cavendish

B
Capernicus

C
Brook Taylor

D
None of these

Solution
Question 9
1 / -0

A small spherical ball of radius $$r$$ falls freely under gravity through a distance of $$h$$ before entering a tank of water. If, after entering the water, the velocity of the ball does not change, then $$h$$ is proportional

A
$$ r^{2}$$

B
$$r^{3}$$

C
$$r^{4}$$

D
$$r^{5}$$

Solution
Question 10
1 / -0

A solid sphere of mass M and radius R is surrounded by a spherical shell of same mass M and radius 2R as shown. A small particle of mass m is released from rest from a height h (<<R) above the shell. There is a hole in the shell.
In what time will it enter the hole at A :-

A
$$2 \frac{\sqrt{hR^2}}{GM}$$

B
$$\sqrt \frac{2hR^2}{GM}$$

C
$$\sqrt \frac{hR^2}{GM}$$

D
None of these

Solution