Gravitational Potential Energy

Q. Two equal point charges of $1\mu C$ each are located at $(\hat{i}+\hat{j}+\hat{k})m$ and $(2\hat{i}+3\hat{j})+\hat{k})m$. The magnitude of the electrostatic force between them is

1. ${10}^{-3}N$
2. ${10}^{-6}N$
3. ${10}^{-9}N$
4. ${10}^{-12}N$

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

Q.

Can potential energy be negative? Explain

Q.

In the figure a potential of 1200V is given to point A and point B is earthed, what is the potential at the point P?

1. 800V

2. 200V

3. 400V

4. 100V

Q. The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half the earth's radius, the orbital velocity will be

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

Q. The figure shows elliptical orbit of a planet $m$ about the sun $S$. The shaded area $\text{SCD}$ is twice the shaded area $\text{SAB}$. If $t_1$ is the time for the planet to move from $\text{C}$ to $\text{D}$ and $t_2$ is the time to move from $\text{A}$ to $\text{B}$, then

1. $t_1=4t_2$
2. $t_1=2t_2$
3. $t_1=t_2$
4. $2t_1=t_2$

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. 

2. 

3. 

4. 

Q.

Power of a water pump is 2 kW. If $g=10m/se{c}^2$ , the amount of water it can raise in one minute to a height of 10 m is

1. 2000 litre

2. 1000 litre

3. 100 litre

4. 1200 litre

Q. The unit of potential energy is

1. $g\left(cm/sec\right)$
2. $g(cm/sec{)}^2$
3. $g\left(c{m}^2/sec\right)$
4. $g\left(cm/se{c}^2\right)$

Q.

A uniform ring of mass M and radius R is placed directly above a uniform sphere of mass 8 M and of same radius R. The centre of the ring is at a distance of $d=\sqrt{3}R$from the centre of the sphere. The gravitational attraction between the sphere and the ring is

1. 

2. 

3. 

4. 

Q. Four identical point masses each equal to M are placed at the four corners of a square of side a. Calculate force of attraction on another point mass m1 kept at the centre of the square

Q.

How to calculate the value of $g$ at the surface of Mars? $(M=0.642x{10}^{24}kg,R=3396km)$

Q. The gravitational field in a region is given by $\overrightarrow{E_g}=(4\hat{i}+\hat{j})\text{N/kg}$. Work done by this field will be zero when the particle is moved along the line

1. $y+4x=2$
2. $4y+x=6$
3. $x+y=5$
4. $x-y=5$

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.

For a satellite escape velocity is 11 km / s. If the satellite is launched at an angle of ${60}^{\circ }$ with the vertical, then escape velocity will be

1. 

2. 

3. 

4. 

Q.

A particle of mass $10g$ is kept on the surface of a uniform sphere of mass $100kg$ and radius $10cm$ Find the work to be done against the gravitational force between them. to take the particle far away from the sphere. $\left(take,G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}\right)$

1. $13.34\times {10}^{-10}J$

2. $3.33\times {10}^{-10}J$

3. $6.67\times {10}^{-9}J$

4. $6.67\times {10}^{-10}J$

Q. In order to shift a body of mass $m$ from a circular orbit of radius $3\text{R}$ to a higher orbit of radius $5\text{R}$ around the earth, the work done is

1. $\frac{3GMm}{5R}$
   
2. $\frac{GMm}{2R}$
   
3. $\frac{GMm}{15R}$
   
4. $\frac{2GMm}{15R}$
   

Q.

What three factors does gravitational potential energy depend on?

Q.

A body weighs 81 N on the surface of the earth. How much will it weigh when taken to a height equal to half of radius of earth.

Q. If $M$ is mass of a planet and $R$ is its radius, then for a planet in order to become black hole $(c$ is speed of light$)$

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

Q. If potential at the surface of earth is assigned zero value, then potential at the centre of earth will be ( mass M, radius R)

Q. The gravitational force between two particles with masses $m$ and $M$, initially at rest at great separation, pulls them together. When their separation becomes $d$, then the speed of either particle relative to the other will be

1. $\sqrt{\frac{G(m+M)}{2d}}$
2. $\sqrt{\frac{G(m+M)}{d}}$
3. $\sqrt{\frac{4G(m+M)}{d}}$
4. $\sqrt{\frac{2G(m+M)}{d}}$

Q.

A boy weighing $25kg$ climbs up from the first floor at a height of $3m$ above the ground to the third floor at a height of $9m$ above the ground. What will be the increase in his gravitational potential energy? (Take $g=10Nk{g}^{-1}$)

Q. An alternating current generator has an internal resistance $R_g$ and an internal reactance $X_g$. It is used to supply power to a passive load consisting of a resistance $R_g$ and a reactance $X_L$. For maximum power to be delivered from the generator to the load, the value of $X_L$ is equal to

1. $X_g$
2. zero
3. $-X_g$
4. $R_g$

Q. A planet of small mass $m$ moves around the Sun of mass $M$ along an elliptical orbit such that its minimum and maximum distances from sun are $r$ and $R$ respectively. Its period of revolution will be:

1. $2\pi \sqrt{\frac{(r+R{)}^3}{6GM}}$
2. $2\pi \sqrt{\frac{(r+R{)}^3}{3GM}}$
3. $2\pi \sqrt{\frac{(r+R{)}^3}{8GM}}$
4. $2\pi \sqrt{\frac{(r+R{)}^3}{GM}}$

Q.

A particle fo mass 100 g is kept on the surface of a uniform sphere of mass 10 kg and radius 10 cm. find the work to be done against the gravitational force between them to take the particle away from the sphere.

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.

The gravitational potential energy of a body depends on its velocity.

1. True
2. False

Q.

The gravitational field in a region is given by $\overrightarrow{E}=\left(5nk{g}^{-1}\right)\overrightarrow{i}+\left(12Nk{g}^{-1}\right)\overrightarrow{j}$ (a) Find the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin. (b) Find the potential at the points (12 m, 0) and (0, 5 m) if the potential at the origin is taken to be zero. (c) Find th echange in gravitational potential energy if a particle of mass 2 kg is taken from the origin to the point (12 m, 5m). (d) Find the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m).

Q. A man is drawing water from a well of depth 10 m using a bucket with hole in it, such that only half of the water remains when bucket arrives at top of the well.
When bucket is full of water, its mass is 40 kg and pulling rate of bucket is constant. The work done by man in kilo joules to pull bucket up is ( g = 10 m/ $s^2$) [ Neglect weight of the bucket.]