Gravitational Potential Energy

Q.

A satellite is revolving around the earth with a kinetic energy$E$. The minimum addition of kinetic energy needed to make its escape from its orbit is

1. $2E$

2. $\surd E$

3. $E/2$

4. $\surd E/2$

5. $E$

Q. Water falls from a height of $60m$ at the rate of $15kg/s$ to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine?$(g=10m/s^2)$

1. $12.3kW$
2. $7.0kW$
3. $8.1kW$
4. $10.2kW$

Q. Two bodies each of mass $M$ are kept fixed with a separation $2L$. A particle of mass $m$ is projected from the midpoint of the line joining their centers, perpendicular to the line. The gravitational constant is $G$. The correct statement(s) is (are)

1. the minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $4\sqrt{\frac{GM}{L}}$
2. the minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $2\sqrt{\frac{GM}{L}}$
3. the minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $\sqrt{\frac{2GM}{L}}$
4. the energy of the mass $m$ remains constant

Q. The gravitational field in a region due to a certain mass distribution is given by $\overrightarrow{E}=(4\hat{i}-3\hat{j})\text{N/kg}.$ The work done by the field in moving a particle of mass $2\text{kg}$ from $(2\text{m},1\text{m})$ to $(\frac{2}{3}\text{m},2\text{m})$ along the line $3x+4y=10$ is

1. $-\frac{25}{3}\text{J}$
2. $-\frac{50}{3}\text{J}$
3. $\frac{25}{3}\text{J}$
4. Zero

Q. Water falls from a height of $60m$ at the rate of $15kg/s$ to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine?$(g=10m/s^2)$

1. $12.3kW$
2. $7.0kW$
3. $8.1kW$
4. $10.2kW$

Q.

A small body starts falling on to the earth from a distance equal to the radius of the earth's orbit. How long will the body take to reach the sun? Express the time in terms of T, period of revolution of the earth round the sun

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

2. $\frac{T}{2\sqrt{2}}$

3. $\frac{T}{\sqrt{2}}$

4. T

Q.

An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential)energy $E_o$. Its potential energy is

1. $-E_o$

2. $1.5E_o$

3. $2E_o$

4. $E_o$

Q. A body of mass m is placed on earth surface is taken to a height of h = 3R, then change in gravitational potential energy is

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

Q. Two bodies each of mass $M$ are kept fixed with a separation $2L$. A particle of mass $m$ is projected from the midpoint of the line joining their centers, perpendicular to the line. The gravitational constant is $G$. The correct statement(s) is (are)

1. the minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $4\sqrt{\frac{GM}{L}}$
2. the minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $2\sqrt{\frac{GM}{L}}$
3. the minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $\sqrt{\frac{2GM}{L}}$
4. the energy of the mass $m$ remains constant

Q. The figure shows the variation of energy with the radius of orbit a body in circular planetary motion. Find the correct statement about the curves A, B and C.

1. A shows the kinetic energy, B the total energy and C the potential energy of the system
2. C shows the total energy, B the kinetic energy and A the potential energy of the system
3. C and A are kinetic and potential energies respectively and B is the total energy of the system
4. A and B are kinetic and potential energies and C is the total energy of the system

Q. How much energy is needed to move a body of ${10}^{3}kg$ mass from Earth's surface to a height of $2R_E$?$(R_E=radiusofEarth=6400km)$

1. $42\times {10}^{9}J$
2. $36\times {10}^{9}J$
3. $64\times {10}^{3}J$
4. $84\times {10}^{3}J$

Q.

A body of mass m kg. starts falling from a point 2R above the earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the eart’s surface [R – Radius of earth, M – Mass of earth, G – Gravitational constant]

1. $\frac{1}{2}\frac{GMm}{R}$

2. $\frac{1}{6}\frac{GMm}{R}$

3. $\frac{2}{3}\frac{GMm}{R}$

4. $\frac{1}{3}\frac{GMm}{R}$

Q.

The gravitational potential energy of a body of mass 'm' at the earth's surface $-mg{R}_e$. Its gravitational potential energy at a height $R_e$ from the earth's surface will be (Here $R_e$ is the radius of the earth)

1. $-2mg{R}_e$

2. $2mg{R}_e$

3. $\frac{1}{2}mg{R}_e$

4. $-\frac{1}{2}mg{R}_e$

Q.

A mass M is split into two parts, m and (M-m), which are then separated by a certain distance. What ratio of $\frac{m}{M}$ maximizes the gravitational force between the two parts

1. $\frac{1}{3}$

2. $\frac{1}{2}$

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

4. $\frac{1}{5}$

Q. The gravitational field in a region due to a certain mass distribution is given by $\overrightarrow{E}=(4\hat{i}-3\hat{j})\text{N/kg}.$ The work done by the field in moving a particle of mass $2\text{kg}$ from $(2\text{m},1\text{m})$ to $(\frac{2}{3}\text{m},2\text{m})$ along the line $3x+4y=10$ is

1. $-\frac{25}{3}\text{J}$
2. $-\frac{50}{3}\text{J}$
3. $\frac{25}{3}\text{J}$
4. Zero

Q. A body of mass $m$ rises to height $h=R/5$ from the earth’s surface, where $R$ is earth’s radius. If $g$ is acceleration due to gravity at earth’s surface, the increase in potential energy is

1. $mgh$
2. $\frac{6}{7}mgh$
3. $\frac{3}{6}mgh$
4. $\frac{5}{6}mgh$