Gravitation Test

Result

Gravitation Test - 79

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

A satellite of mass $$'m'$$ is revolving around the earth in an orbit of radius $$10R$$ ($$R$$ is the radius of earth), the minimum energy required to give the satellite so that it can escape the gravitational field of the earth is [mass of earth$$=M_e$$]:

A
$$\dfrac{{G{M_e}m}}{{20R}}$$

B
$$\dfrac{{G{M_e}m}}{{10R}}$$

C
$$\dfrac{{G{M_e}m}}{{R}}$$

D
$$\dfrac{{G{M_e}m}}{{2R}}$$

Solution
Question 2
1 / -0

At what depth below the surface of the earth, is the value of $$g$$ same as that at a height of $$10\ km$$ from the surface of the earth?

A
$$5\ km$$

B
$$10\ km$$

C
$$20\ km$$

D
$$40\ km$$

Solution
Question 3
1 / -0

If $$K$$ is the kinetic energy of the earth and $$P$$ is the gravitational potential energy of the earth as it revolves around the sun, then which of the following statements is true?

A
$$K = 2P$$

B
$$P = -K$$

C
$$P = -2K$$

D
$$P = -K/2$$

Solution
Question 4
1 / -0

If the gravitational acceleration at the Earth's surface is $$9.81\,m{s^{ - 2}}$$, what is its value at a height equal to the diameter of the Earth from its surface?

A
$$4.905\,m{s^{ - 2}}$$

B
$$2.42\,m{s^{ - 2}}$$

C
$$3.27\,m{s^{ - 2}}$$

D
$$1.09\,m{s^{ - 2}}$$

Solution
Question 5
1 / -0

A planet in a distant solar system is $$10$$ times more massive then the earth and its radius is $$10$$ times smaller. Give that escape velocity from the earth is $$11\ km/s$$, the escape velocity from the surface of the plants is

A
$$100\ k m / s$$

B
$$110\ k m / s$$

C
$$120\ k m / s$$

D
$$130\ k /m s$$

Solution

Escape velocity $$= \sqrt{\dfrac{2GM}{R}}$$
$$\sqrt{\dfrac{2GN}{R}}=11 $$ (given)
$$M \longrightarrow 10\ M$$
$$R \longrightarrow R/10$$
Putting value
$$Vc= \sqrt{\dfrac{2G (10\ m) \times 10}{R}}$$
$$=10 \times \sqrt{\dfrac{2GM}{R}}$$
$$=110\ w/s$$
Question 6
1 / -0

Choose the correct answer:
The height over the surface of the earth at which the gravitational field of the earth becomes $$\frac{1}{4}$$th of the field at the surface

A
$$\sqrt2 R$$

B
$$\frac{R}{\sqrt2}$$

C
R

D
$$(\sqrt2 - 1)R$$
Question 7
1 / -0

The kinetic energy needed to project a body of mass m from the earth's surface (radius $$R$$) to infinity is -

A
$$\frac{mgR}{2}$$

B
$$2mgR$$

C
$$mgR$$

D
$$\frac{mgR}{4}$$

Solution
Question 8
1 / -0

A rubber ball is dropped from a height of $$5$$cm on a plane, where the acceleration due to gravity is not shown. On bouncing it rises to $$1.8$$m. The ball loses its velocity on bouncing by a factor of?

A
$$\dfrac{16}{25}$$

B
$$\dfrac{2}{5}$$

C
$$\dfrac{5}{3}$$

D
$$\dfrac{9}{25}$$

Solution

$$\dfrac { \dfrac { 1 }{ 2 } { { mv }_{ 1 } }^{ 2 } }{ \dfrac { 1 }{ 2 } { { mv }_{ 2 } }^{ 2 } } =\dfrac { mg{ h }_{ 1 } }{ mg{ h }_{ 2 } } =\dfrac { 25 }{ 9 } $$

$$\dfrac { { { v }_{ 1 } }^{ 2 } }{ { { v }_{ 2 } }^{ 2 } } =\dfrac { 25 }{ 9 } $$

$$\dfrac { { v }_{ 1 } }{ { v }_{ 2 } } =\dfrac { 5 }{ 3 } $$
Question 9
1 / -0

A man slides down a light rope whose breaking strength $$\eta$$ times the weight $$(\eta < 1)$$. The maximum acceleration of the man so that the rope just breaks is:-

A
$$g(1 - \eta)$$

B
$$g(1 +\eta)$$

C
$$g\eta$$

D
$$\dfrac{g}{\eta}$$

Solution

Breaking strength $$=$$ $$-$$ maximum tension
Given that
$$T=\eta \times $$ weight of man $$=\eta \times mg$$
From Newton's law of motion
$$mg-T=ma$$
$$mg-\eta mg=ma$$
$$mg\left( 1-\eta \right) =ma$$
$$a=\left( 1-\eta \right) g$$
Given that, $$\eta <1$$. So, acceleration is downwards because $$\left( 1-\eta \right) >0$$
So, $$a=\left( 1-\eta \right) g$$ option (A) correct.
Question 10
1 / -0

The depth at which the effective value of acceleration due to gravity is one fourth that of its value on the earth's surface is

A
R

B
$$\dfrac{3R}{4}$$

C
$$\dfrac{R}{2}$$

D
$$\dfrac{R}{4}$$

Solution