Potential Energy of an Object at a Height

Q.

The escape velocity $v$ of a body depends upon ($1$) the acceleration due to gravity $\left(g\right)$ of the planet and (2) the radius $\left(R\right)$ of the planet. Use the method of dimensions to obtain a relation between $v$, $g$, and $R$.

Q.

A man of mass 50 kg climbs up a ladder of height 10 m. Calculate:

(i) the work done by the man, and

(ii) the increase in his potential energy. (g = 9.8 m $s^{-2}$).

Q.

An asteroid is moving directly towards the centre of the Earth. When at a distance of $10R$ ( $R$ is the radius of the Earth ) from the Earths centre, it has a speed of $12km/s$. Neglecting the effect on Earths atmosphere, what will be the speed of the asteroid when it hits the surface of the Earth ( escape velocity from the Earth is $12km/s$ )? Give your answer to the integer in $km/s$.

Q.

A $200kg$ satellite is revolving around the earth in a circular orbit of radius $2r$. The amount of energy required to transfer it to a circular orbit of radius $4r$ is $[m_e=6x{10}^{24}kg,r=6.4\times {10}^{6}m]$

Q.

We say that gravitational potential energy is zero when the object is on the ground(earth surface). My doubt is that can gravitational potential energy be considered zero anywhere (at any altitude) when object is kept on the surface of earth? And also there is distance between the object and the centre of the earth, how can the gravitational potential energy be considered zero?

Q.

How much energy is gained by a box of mass 20 kg when a man

(a) carrying the box waits for 5 minutes for a bus?

(b) runs carrying the box with a speed of 3 m $s^{-1}$ to catch the bus?

(c) raises the box by 0.5 m in order to place it inside the bus?(g=10 m $s^{-2}$).

Q.

A planet is having a mass twice to that of earths mass and its radius as 4 times that of earths radius. Determine the acceleration due to gravity at the surface of this planet. Acceleration due to gravity at earths surface is $10{\text{ms}}^{-2}$.

Q.

If an object of mass$m$ is taken from the surface of earth (radius $R$) to a height $2R,$ then the work done is

1. $2mgR$

2. $mgR$

3. $\left(\frac{2}{3}\right)mgR$

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

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

Q.

The decrease in the potential energy of a ball of mass $20kg$which falls from a height of$50cm$ is

1. $968J$

2. $98J$

3. $1980J$

4. None of these

Q.

Two bodies, A and B of equal mass are kept at heights 20 m and 30 m respectively. Calculate the ratio of their potential energies.

1. 3:2

2. 2:1

3. 2:3

4. 4:9

Q.

Earth exerts gravitational force on the moon, keeping it in its orbit. The reaction to this force in the sense of Newtons third law is.

1. The centripetal force on the moon.

2. The gravitational force on earth by the moon

3. The tides due to the moon

4. None of the above

Q.

A body of mass 5 kg falls from a height of 10 m to 4m. Calculate:

(i) the loss in potential energy of the body, and (ii) the total energy possessed by the body at any instant? (Take g=10 m $s^{-2}$).

Q.

A vessel containing 50 kg of water is placed at a height of 15 m above the ground.Assuming the gravitational potential energy at ground to be zero, what will be the gravitational potential energy, of water in the vessel?(g=10 m $s^{-2}$)

Q.

During sunrise or sunset, the sun appears bigger because the rays of light coming from it pass through :

1. larger length of atmosphere

2. smaller length of atmosphere

3. the earth gets closer to sun

4. none of these

Q.

Name the form of energy which a body may possess even when it is not in motion.Give an example to support your answer.

Q.

Light causes the sensation of

1. Vision

2. touch

3. smell

4. taste

Q.

Explain Center of Mass.

Q.

A body is thrown vertically up from the earth’s surface. What happened to its P.E during the motion?

1. Increases

2. Decreases

3. Remains constant

4. First increases then decrease

Q.

A rod of length $1m$ pivoted at one end is released from rest when it makes $30°$ from the horizontal as shown in the figure below.If $\omega$ of rod is $\sqrt{n}$ at the moment it hits the ground, then find $n$.

Q.

Suppose the distance between earth and sun becomes half of its present distance. What is likely to happen to life?

Q.

Why is gravitational mass equal to inertial mass?

Q.

Who is the WhatsApp founder?

Q.

Find the percentage change in acceleration due to gravity at a height of 32 km from the surface of the earth.

1. $3\%$

2. $5\%$

3. $8\%$

4. $1\%$

Q.

Calculate the height through which a body of mass 0.5 kg is lifted if the energy spent in doing so is 1.0 J.Take g=10 m $s^{-2}$.

Q.

A mango is falling from the branch of a tree at a height h from the ground. After it has fallen a height of $\frac{h}{2}$, it will possess:

1. only potential energy.

2. only kinetic energy.

3. half kinetic and half potential energy.

4. more kinetic and less potential energy.

Q. A particle of mass $m$ is projected from the surface of earth with a speed $V_0$ ($V_0$ < escape velocity). The speed of the particle at a height h$=$R (radius of the earth) is

1. $\sqrt{gR}$
2. $\sqrt{V_0^2-2gR}$
3. $\sqrt{V_0^2-gR}$
4. none of these

Q.

A uniform chain of mass m and length l is lying on the table such that its one-fifth part is hanging from the edge of the table. What minimum work is required to lift this part of the chain on the table?

Q. The sun appears to us ________ minutes earliear than the actual sunrise and ________ minutes later than the actual sunset.

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

Q. A body of mass $5kg$ falls from a height of $10m$ to $4m$. Calculate the loss in potential energy of the body. (Take $g=10m{s}^{-2}$).

1. $0J$
2. $300000J$
3. $3J$
4. $300J$

Q.

When two different stones of masses 1 kg and 2 kg are taken to the same heights, then:

1. The potential energy of the stone of mass 1 kg is more than that of the 2 kg stone.

2. The potential energy of the stone of mass 2 kg is more than that of the 1 kg stone.

3. The potential energy of both the stones would be the same.

4. Cannot be judged with the given information.