Gravtiational PE

Q. A particle is released from height $S$ from the surface of the Earth. At a certain height, its kinetic energy is three times of its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively

1. $\frac{S}{4},\sqrt{\frac{3gS}{2}}$
2. $\frac{S}{4},\sqrt{3gS}$
3. $\frac{S}{4},\frac{\sqrt{gS}}{2}$
4. $\frac{S}{2},\frac{\sqrt{3gS}}{2}$

Q.

A block of mass 10kg is moving in x-direction with a constant speed of 10 m/s. It is subjected to a retarding force F = -0.1 x J/m during its travel from x = 20 m to x = 30 m. Its final kinetic energy will be

1. 475 J

2. 450 J

3. 275 J

4. 250 J

Q.

A uniform chain of mass $M$ and length $L$ is held on a horizontal frictionless table with $\frac{1}{n^{th}}$ of its length hanging over the edge of the table. The work done is pulling the chain up on the table is

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

2. $\frac{MgL}{n}$

3. $\frac{MgL}{n^2}$

4. $\frac{MgL}{2n^2}$

Q.

Binding energy of a satellite is

Q.

Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy?

Q.

A ball of mass $0.2\mathrm{Kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2\mathrm{m}$ while applying the force and the ball goes up to $2\mathrm{m}$ height further, find the magnitude of the force. (take, $\mathrm{g}=10\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$)

1. $4\mathrm{N}$

2. $16\mathrm{N}$

3. $20\mathrm{N}$

4. $22\mathrm{N}$

Q.

Define potential energy?

Q. Gravitational potential in a region is given by $V=-(x+y+z)\text{J/kg}$. Find the gravitational field intensity at $(2,2,2)$.

1. $(\hat{i}+\hat{j}+\hat{k})\text{N/kg}$
2. $2(\hat{i}+\hat{j}+\hat{k})\text{N/kg}$
3. $3(\hat{i}+\hat{j}+\hat{k})\text{N/kg}$
4. $4(\hat{i}+\hat{j}+\hat{k})\text{N/kg}$

Q.

A chain of length l an mass m lies on the surface of a smooth sphere of radius R>l with one end tied to the top of the sphere. (a) Find the gravitational potential energy of the chain with reference level at the centre of the sphere. (b) Suppose the chain is released and slides down the sphere. Find the kinetic energy of the chain, when it has slid through an angle $\theta$ (c) Find the tangential acceleration $\frac{dv}{dl}$ of the chain when the chain starts sliding down.

Q.

If $g$ is the acceleration due to gravity on the earths surface, the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

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

2. $2mgR$

3. $mgR$

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

Q.

The ratio of the energy required to raise a satellite upto a height h above the surface of earth to that the kinetic energy of the satellite into the orbit there is (R= radius of earth)

1. h : R

2. R : 2h

3. R : h

4. 2h : R

Q. A particle of mass 10g is describing S.H.M along a straight line with period of 2s and amplitude of 10cm. Its kinetic energy when it is at 5cm from its equilibrium position is

1. 
2. 
3. 
4. 

Q.

An ideal spring is hung vertically from the ceiling. When a 2kg mass hangs at rest the spring is elongated by 6cm from its relaxed length. A downward force is now applied to the mass to elongate the spring further by 10cm. When the spring is elongated by force, the work done by the spring is

1. 36J

2. -3.6J

3. 4.26J

4. -4.26J

Q. When will be the potential energy be negative?

Q. Please explain why mgh/ 1+h/R is the change in potential energy when a body is raised to height h from earth's surface

Q.

A pump is required to lift 1000 kg of water per minute from a well 20 m deep and eject it at a rate of 20 m/s.

(x) How much work is done in ejecting water?

(y) How much work is done in lifting water?

(z) What HP (horse power) engine is required for the purpose of lifting water?

(1) 2 $\times$${10}^5$ $\frac{j}{min}$ (2) 4 $\times$${10}^5$ $\frac{j}{min}$ (3) 3 $\times$${10}^5$ $\frac{j}{min}$

(4) 6.6 $\times$${10}^3$ $\frac{j}{s}$ (5) 8 $\times$${10}^4$ watts (6)${10}^5$ watts

Take g = $\frac{10m}{s^2}$

1. x - 2, y - 1, z - 6

2. x - 1, y - 1, z - 4

3. x - 1, y - 2, z - 5

4. x - 1, y - 1, z - 6

Q.

The gravitational potential energy of an object is due to

1. its mass

2. ts acceleration due to gravity

3. its height above the earth’s surface

4. all of the above

Q.

Water falling from a 50 m high fall is to be used for generating electric energy. If $1.8\times {10}^{\circ }$ kg of water falls per hour and half the gravitational potential energy can be converted into electric energy, how many 100 2 lamps can be lit ?

Q.

A mass M is lowered with the help of a string by a distance h at a constant acceleration $\frac{g}{2}$. The work done by string will be

1. 

2. 

3. 

4. 

Q.

A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with period

1. 

2. 

3. 

4. 

Q. A bread gives a boy of mass 40kg an energy of 21kJ. If the efficiency is 28%, then the height that can be climbed by him using this energy, is:

1. 22.5m
2. 10m
3. 5m
4. 15m

Q.

Define potential energy. On what factors does potential energy depend.

Q.

What are the two types of potential energy? Give two examples of each.

Q. A body moves over one-fourth of a circular arc in a circle of radius $r$. The magnitude of distance travelled and displacement will be respectively

1. $\frac{\pi r}{2},r\sqrt{2}$
2. $\frac{\pi r}{4},r$
3. $\pi r,\frac{r}{\sqrt{2}}$
4. $\pi r,r$

Q.

When an object is dropped from a height, its potential energy ______ and its kinetic energy ______ till it reaches the ground.

Q.

A uniform chain of mass $m$ and length $l$ is lying on a frictionless horizontal table with one-third of its length hanging over the edge of the table. The amount of work done to pull the hanging part of the chain up to the table is given by

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

2. $\frac{mgl}{6}$

3. $\frac{mgl}{9}$

4. $\frac{mgl}{18}$

Q.

An insect of mass m crawls along the hanging thread with an acceleration a =$\frac{g}{2}$. The normal reaction offered by ground on the block of mass 2m kept stationary on ground is

1. mg

2. mg

3. mg

4. 2 mg

Q.
$P\to \text{Solid sphere},Q\to \text{Solid cube},R\to \text{Solid cone},S\to \text{Solid cylinder}$

Assuming potential energy ${}^{\prime }{U}^{\prime }$ at the ground level to be zero.
All objects are made of the same material.
$U_P=\text{Potential energy of solid sphere}$
$U_Q=\text{Potential energy of solid cube}$
$U_R=\text{Potential energy of solid cone}$
$U_S=\text{Potential energy of solid cylinder}$
Identify the correct option(s).

1. $U_S>U_P$
2. $U_Q>U_S$
3. $U_P>U_Q$
4. $U_P>U_S$

Q.

A person is painting has house walls. He stands on a ladder with a bucket containing paint in one hand and a brush in other. Suddenly the bucket slips from his hand and falls down on the floor. If the bucket with the paint had a mass of 6.0 kg and was at a height of 2.0 m at the time it slipped, how much gravitational potential energy is lost together with the paint ?

Q.

The kinetic energy of moon with respect to earth is K. The magnitude of gravitational potential energy of the moon earth system is U with zero potential energy at infinite separation is,

1. U<K

2. Either (b) or (c)

3. U>K

4. U=K