Gravitational Potential

Q.

What is the importance of the universal law of Gravitation?

Q.

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

1. 

2. 

3. 

4. 

Q. The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is

1. 
2. 
3. 
4. 

Q. The quarter disc of radius $R$ (see figure) has a uniform surface charge density $\sigma$.
The $Z$ component of electric field at $(0,0,Z)$ is found to be $E_Z=\frac{\sigma }{f{ϵ}_0}[1-\frac{Z}{\sqrt{R^2+Z^2}}]$
Then, the value of $2f$ is

Q. The ratio of orbital speeds of two satellites, if the ratio of their time period is $8:1$ are

1. $\frac{(V_O{)}_1}{(V_O{)}_2}=\frac{4}{1}$
   
2. 
   $\frac{(V_O{)}_1}{(V_O{)}_2}=\frac{1}{2}$
3. $\frac{(V_O{)}_1}{(V_O{)}_2}=\frac{1}{4}$
4. 
   $\frac{(V_O{)}_1}{(V_O{)}_2}=\frac{2}{1}$

Q. A satellite is orbiting around earth in a circular orbit of radius $r$. A particle of mass $m$ is projected from satellite in forward direction with velocity $v=\sqrt{\frac{2}{3}}$ times orbital velocity (this velocity is given with respect to earth). During subsequent motion of the particle, its minimum distance from the centre of earth is

1. $\frac{r}{2}$
   
2. $\frac{r}{3}$
3. $\frac{2r}{3}$
4. $\frac{4r}{5}$

Q. Two satellites of masses $400\text{kg}$ and $500\text{kg}$ are revolving around earth in different circular orbits of radii $r_1$ and $r_2$ such that their kinetic energies are equal. The ratio of $r_1$ to $r_2$ is

1. $4:5$
2. $16:25$
3. $5:4$
4. $25:16$

Q. A body of mass m is taken to a height kR from the surface of the earth very slowly, R being the radius of the earth. Find the change in gravitational potential energy in this process.

Q.

A body of mass m is taken from earth surface to the height h equal to radius of earth. The increase in potential energy will be

1. 

2. 

3. mgR

4. 

Q. A body is projected horizontally near the surface of the earth with $\sqrt{1.5}$ times the orbital velocity. The maximum height up to which it will rise above the surface of the earth is 'n' times the radius of earth, then find the value of n.

Q. A particle of mass M is situated at the centre of spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be

1. $-\frac{3GM}{a}$
2. $-\frac{2GM}{a}$
3. $-\frac{GM}{a}$
4. $-\frac{4GM}{a}$

Q.

The force experienced by a unit mass at a point in the gravitational field is called its

1. gravitational intensity

2. electric intensity

3. magnetic intensity

4. gravitational constant

Q. Assertion :Gravitational potential is maximum at infinity. Reason: Gravitational potential is the amount of work done to shift a unit mass from infinity to a given point in gravitational attraction force field.

1. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
2. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
3. STATEMENT-1 is True, STATEMENT-2 is False
4. STATEMENT-1 is False, STATEMENT-2 is True

Q. Consider two point masses m and 2m ata distance of 3m in a gravity free space. Find the maximum possible velocity v which can be given to 2m so that 2m and m revolve in a closed orbit due to their mutual gravitation force of attraction.

Q. A diametrical tunnel is dug across the earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reaches the centre of the earth is

1. 
2. 
3. 
4. 

Q.

If velocity $\left(v\right)$, time $\left(t\right)$, and mass $\left(m\right)$ are taken as fundamental quantities, then the dimensional formula for gravitational potential would be___

Q. The potential energy of a particle of mass $1\text{kg}$ is, $U=10+(x-2{)}^2$. Here, $U$ is in $\text{joule}$ and $x$ in $\text{metre}$ on the positive $x-$axis. Particle travels upto $x=+6\text{m}$. Choose the correct statement.

1. On negative $x-$axis particle travels upto $x=-2\text{m}$
2. The maximum kinetic energy of the particle is $16\text{J}$
3. Both $\left(a\right)$ and $\left(b\right)$ are correct
4. Both $\left(a\right)$ and $\left(b\right)$ are wrong

Q. The gravitational potential is a

1. scalar
2. scalar or vector depending on the situation
3. vector
4. scalar based on the mass of the particle

Q. The SI unit of gravitational potential is

1. $J$
2. $Jk{g}^{-1}$
3. $Jkg$
4. $Jk{g}^{-2}$

Q. Two satellites, $A$ and $B$, have masses $m$ and $2m$ respectively. $A$ is in a circular orbit of radius $R$, and $B$ in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $\frac{T_A}{T_B}$, is:

1. $\frac{1}{2}$
2. $2$
3. $\sqrt{\frac{1}{2}}$
4. $1$

Q. A diametrical tunnel is dug across the earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reaches the centre of the earth is

1. $\sqrt{0.5gR}$
2. $\sqrt{gR}$
3. $\sqrt{2.5gR}$
4. $\sqrt{7.1gR}$

Q. The universal law of gravitation must be applicable to

1. The earth and the moon.
2. The planets around the Sun.
3. Any pair of bodies.
4. The earth and the apple.

Q. A uniformly charged sphere is placed in such a way that center of sphere coincides with origin, potential of surface is $V_0$. On x axis, we have n points those having potential $\frac{5V_0}{4}$, find "n"

1. 4
2. 3
3. 2
4. 1

Q. If mass of earth is $M$, radius is $R$ and gravitational constant is $G$, then work done to take $1kg$ mass from earth surface to infinity will be:

1. $\frac{GM}{2R}$
2. $\sqrt{\frac{GM}{2R}}$
3. $\frac{GM}{R}$
4. $\sqrt{\frac{2GM}{R}}$

Q. A body on earth, is weighed at the poles and then at the equator. The weight

1. at the equator will be greater than the weight at the poles.
2. at the poles will be greater than the weight at the equator.
3. at the poles will be equal to the weight at the equator.
4. depends upon the object.

Q. What is the geometrical interpretation of infinity for gravitational field and gravitational potential?

Q. A satellite moving around earth at a height $R$ (radius of earth) from the surface of earth needs to be put into another circular orbit of radius $8R$. How much more energy needs to be provided to take the satellite to the new orbit? ($M_e$ is mass of the earth and $m$ is mass of satellite).

1. $\frac{3G{M}_{e}m}{16R}$
2. $\frac{G{M}_{e}m}{10R}$
3. $\frac{3G{M}_{e}m}{20R}$
4. $\frac{2G{M}_{e}m}{R}$

Q.

We assume that earth is at zero potential because capacitance of the earth is

1. infinite
2. ${10}^{6}Farad$
3. zero
4. cannot say

Q. The gravitational potential difference between the surface of planet and a point 20 m above its surface is $2Jk{g}^{-1}$ If the gravitational field over this range is uniform, then the work done to raise the body of 5 kg from the surface to a height of 4 m is:

1. 1 J
2. 2 J
3. 4 J
4. 8 J

Q.

Two masses 90 kg and 160 kg are at a distance 5 m apart. Compute the magnitude of intensity of the gravitational field at a point distance 3m from the 90 kg and 4m from the 160 kg mass. G=6.67 $\times$ ${10}^{-11}$SI units..

1. 9.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

2. 4.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

3. 6.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$

4. 0.43 $\times$ ${10}^{-10}$ N $k{g}^{-1}$