Universal Law of Gravitation

Q.

Two particles of equal mass $m$ go around a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle with respect to their center of

Q. If the distance between two bodies is doubled, what happens to the gravitational force of attraction between the bodies?

1. doubles
2. reduces to half
3. remains constant
4. reduces to one-fourth

Q.

An apple falls from a tree because of gravitational attraction between the earth and the apple. If ${\mathrm{F}}_1$ is the magnitude of force exerted by the earth on the apple and ${\mathrm{F}}_2$ is the magnitude of force exerted by the apple on the earth, then

1. ${\mathrm{F}}_1$ is very much greater than ${\mathrm{F}}_2$

2. ${\mathrm{F}}_1$ is only a little greater than ${\mathrm{F}}_2$

3. ${\mathrm{F}}_1$ is only a little greater than ${\mathrm{F}}_2$

4. ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ are equal

Q.

The masses of the earth and moon are $6\times {10}^{24}kg$ and $7.4\times {10}^{22}kg$, respectively. The distance between them is $3.84\times {10}^{5}m$. Calculate the gravitational force of attraction between the two. Use $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

1. $1\times {10}^{26}N$
2. $2\times {10}^{26}N$
3. $4\times {10}^{26}N$
4. $3\times {10}^{26}N$

Q.

The force of gravitation between two bodies in the universe does not depend on:

1. the distance between them

2. the product of their masses

3. the sum of their masses

4. gravitational constant

Q.

State two applications of universal law of gravitation.

Q.

Two planets of radii $r_1$ and $r_2$ are made from the same material. The ratio of the acceleration due to gravity $\frac{g_1}{g_2}$ at the surface of the two planets is

1. r₁/r₂

2. ( r₁/r₂)²

3. (r₂/r₁)²

4. r₂/r₁

Q. It is seen that falling apple is attracted towards the Earth. We all know that apple will also exert an equal and opposite force on the Earth. If so, we don’t see Earth moving towards the apple, why?

1. The mass of apple is negligibly small compared to that of the Earth.
2. The acceleration produced by the apple on the Earth would be negligible.
3. Cannot be determined with the given information
4. The force acting on both that is on apple and Earth is equal.

Q.

Given mass of earth =$6.4\times {10}^{24}$ kg , radius of earth = $6.4\times {10}^6$ m. Calculate the force of attraction experienced by a man of mass 50 kg.

Q. The mass of the earth is $6\times {10}^{24}kg$. The distance between the earth and the Sun is $1.5\times {10}^{11}m$. If the gravitational force between the two is $3.5\times {10}^{22}N$, what is the mass of the Sun? Use $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

1. $1.96\times {10}^{30}kg$
2. $1.2\times {10}^{12}kg$
3. $3.6\times {10}^{18}kg$
4. $2.4\times {10}^{9}kg$

Q. If the gravitational force between two spheres is $400N$, and the distance between them is doubled, the force will be ____________

1. $400N$
2. $200N$
3. $100N$
4. 
   $40N$

Q. Two asteroids exert a gravitational force, F, on each other. Some time later, the asteroids are now three times as far from each other as before. Which of the following represents the gravitational force at this distance?

1. F/3
2. F/6
3. F/9
4. F/2

Q. The radius of planet $A$ is half the radius of planet $B$. If the mass of $A$ is $M_A$, what must be the mass of $B$ so that the value of $g$ on $B$ is half that of its value on $A$?

1. $3M_A$
2. $4M_A$
3. $M_A$
4. $2M_A$

Q. A mass of 5 kg is held at a position 2 m away from a mass of 10 kg. What is the gravitational attraction between the two masses?
Take value of $G$ as $6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

1. $8.3\times {10}^{-10}N$
2. $4.2\times {10}^{-10}N$
3. $9.7\times {10}^{-10}N$
4. $5.7\times {10}^{-10}N$

Q.

A ring of mass m and radius R and a sphere of mass M and same radius R are separated by a distance $\sqrt{8}R$ as shown in the figure. The force of attraction between the ring and the sphere is

1. $\frac{2\sqrt{2}}{27}\frac{GmM}{R^2}$

2. $\frac{GmM}{8R^2}$

3. $\frac{GmM}{9R^2}$

4. $\frac{\sqrt{2}}{9}\frac{GmM}{9R^2}$

Q.

Two spheres have masses in the ratio 2:3 but have same gravitational PE. Calculate the ratio of their heights & weights.

1. Height Ratio is 3:2 and Weight Ratio is 2:3

2. Height Ratio is 2:3 and Weight Ratio is 2:3

3. Height Ratio is 3:2 and Weight Ratio is 3:2

4. Height Ratio is 2:3 and Weight Ratio is 3:2

Q.

If the distance between the earth and the moon is reduced to half of its original, the gravitational force between them will _________.

Q.

State whether the following statement is true or false.

Value of G is different on the earth and the moon.

1. True
2. False

Q.

Two stones lying on the surface of the Earth have mass, a gravitational force will always exist between them and it will try to pull the stones towards each other. But actually, we don’t see the stones moving towards each other, why?

Statement 1: The acceleration because of gravitational force is in the range of ${10}^{-12}$ $m{s}^{-2}$.

Statement 2: Stones are lying on a flat surface, so they cannot move.

Statement 3: The force of friction is much higher than the gravitational force.

Statement 4: The stones are irregular in shape, so they cannot move.

Which statements explains the reason for the above question?

1. Statement 1 and 2 are the reasons

2. Statement 1 and 3 are the reasons

3. Only statement 4 is the reason

4. Statement 3 and 4 are the reasons

Q.

The masses of two planets are in the ratio 1: 2. Their radii are in the ratio 1: 2. The acceleration due to gravity on the planets is in the ratio.

1. 1: 2

2. 2: 1

3. 3: 5

4. 5: 3

Q.

The universal law of gravitation is valid for

1. Spherical bodies

2. Elliptical bodies

3. Any arbitrary- shaped bodies

4. Rectangular objects

Q. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
[3 marks]

Q. Calculate the escape velocity (in ${\text{km s}}^{-1}$) of Neptune. The mass of Neptune $\approx {10}^{26}\text{kg}$, radius of Neptune, $\approx 24,170\text{km}$

1. 23.5

Q.

Determine gravitational attraction between two asteroids separated by $22000$$\text{m}$ if their masses are $450000$$\text{kg}$ and $700000\text{kg}$ respectively.

1. $1.2\times {10}^{-6}$N

2. $1.2\times {10}^{-8}$N

3. $4.3\times {10}^{-8}$N

4. $2.8\times {10}^{-6}$N

Q.

The universal constant of gravitation G has the unit?

1. N

2. m/s

3. Nm²/kg²

4. J

Q.

Consider a heavily body which has a mass twice that of the earth and a radius thrice that of the earth. What will be the weight of the book on this heavily body, if its weight on earth is 900 N?

Q.

If mass and radius of the Earth are $6.0\times {10}^{24}$ kg and $6.4\times {10}^6$ m respectively, calculate the force exerted by the Earth on a body of mass 1 kg. Also, calculate acceleration produced in the body of mass 1 kg and acceleration produced in the Earth.

The accelerations of 1 kg mass and Earth are:

1. 9.8 $\frac{m}{s^2}$ and 1 $\frac{m}{s^2}$ respectively

2. 9.8 $\frac{m}{s^2}$ and $1.63\times {10}^{-24}$ $\frac{m}{s^2}$ respectively

3. $1.63\times {10}^{-24}$ $\frac{m}{s^2}$ and 9.8 $\frac{m}{s^2}$ respectively

4. 9.8 $\frac{m}{s^2}$ for both

Q.

Two spheres have masses in the ratio 2:3 but have same gravitational PE. Calculate the ratio of their heights & weights.

1. 3:2, 2:3

2. 2:4, 4:2

3. 4:8, 8:4

4. 7:2, 2:7

5. 1:6, 6:1

Q. Which physical quantity has the unit $Wb/m^2$? Is it a scalar or a vector quantity?

Q. (A) How do you explain that an object is in uniform circular motion
(B) Calculate the acceleration of the moon towards earth's center.