Gravtiational PE

Q.

A ball dropped from a height of $2m$rebounds to a height of $1.5m$ after hitting the ground. Then, the percentage of energy lost is

1. $25$

2. $30$

3. $50$

4. $100$

Q.

Work done in raising a box depends on:

1. How fast it is raised

2. The strength of the man

3. The height by which it is raised

4. None of the above

Q. a particle of mass m in a unidirectional potentil field have potential energy U(x)=α+2β x^2 where α andβ are positive cons†an t.find its time period of oscilltion

Q.

One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is $\frac{1}{2}k{x}^2$. The possible cases are

1. The spring was initially compressed by a distance x and was finally in its natural length

2. It was initially stretched by a distance x and finally was in its natural length

3. It was initially in its natural length and finally in a compressed position

4. It was initially in its natural length and finally in a stretched position

Q.

A body of mass m = 1 kg is dropped from a height h = 40 cm on a horizontal platform fixed to one end of an elastic spring, the other being fixed to a base as shown in the figure. As a result, the spring is compressed by an amount x = 10 cm. What is the force constant of the spring? Take $g=10m{s}^{-2}$.

1. $600N{m}^{-1}$

2. $800N{m}^{-1}$

3. $1000N{m}^{-1}$

4. $1200N{m}^{-1}$

Q. A man weighing 50 kg f supports a body of 25 kg f on his head. what is the work done when he moves a dis†an ce of 20m up an incline of 1 in 10. take g=9.

Q. 18.A ball is thrown vertically upwards with certain initial velocity. Assume that there is no air resistance. Draw the following graph- Kinetic energy V/S Time

Q.

Water is drawn from a well in a 5 kg drum of capacity 55 L by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kg$m^{-1}$. The work done in lifting water to the ground from the surface of water in the well 20 m below is [g = 10 m$s^{-2}$]

1. 18 J

2. 9.8×10×6 J

3. 1.5×10⁴ J

4. 1.4×10⁴ J

Q.

In the given figure, what is the work done by the spring force?

1. 

2. 

3. 

4. 

Q. 84. why the work done by gravitational force of sun during motion of a planet from perihelion to aphelion is negative?

Q. A block (B) is attached to two upstretched springs $S_{1}and{S}_2$ with spring constants k and 4k, respectively. The other ends are attached to two supports $M_{1}and{M}_2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere.

Q.

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is [IIT 1985]

1. $MgL$

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

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

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

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.

The gravitational field in a region is given by $\overline{E}=\left(20Nk{g}^{-1}\right)(\hat{i}+\hat{j})$.Find the gravitational Potential at the origin (0, 0) in $Jk{g}^{-1}$

1. 20V

2. 0

3. 50V

4. 10V

Q. A ball of mass $600\text{g}$ is dropped to the ground from a height of $25\text{m}$. If the energy of the ball reduces by $35\%$ after striking the ground, what is the height to which it rebounds?

1. $20\text{m}$
2. $16.25\text{m}$
3. $17.16\text{m}$
4. $18.02\text{m}$

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. $\frac{MgL}{n}$

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

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

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

Q. You lift a heavy book from the floor of the room and keep it in the book shelf having a height 2 m. In this process you take 5 seconds. The work done by you will depend upon-

1. Mass of the book and time taken
2. Weight of the book and height of the book shelf
3. Height of the book shelf and time taken
4. Mass of the book, height of the book shelf and time taken.

Q.

A body of mass m = 1 kg is dropped from a height h = 40 cm on a horizontal platform fixed to one end of an elastic spring, the other being fixed to a base as shown in the figure. As a result, the spring is compressed by an amount x = 10 cm. What is the force constant of the spring? Take $g=10m{s}^{-2}$.

1. $600N{m}^{-1}$

2. $800N{m}^{-1}$

3. $1000N{m}^{-1}$

4. $1200N{m}^{-1}$

Q. A block (B) is attached to two upstretched springs $S_{1}and{S}_2$ with spring constants k and 4k, respectively. The other ends are attached to two supports $M_{1}and{M}_2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere.

Q.

Which of the following is not an example of zero work?

1. When a horse pulls a cart on a level road.

2. The work done by a coolie when he travels on a horizontal platform, with a load on his head.

3. When a person holds some amount of load but, does not move from his position.

4. The work done by the tension in the string, when a body tied with the string move along a circular path.

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 uniform rod of mass 2kg and length 1m is lying on a horizontal surface. if the work done in raising one end of the rod through an angle 45⁰ is W, the work done in raising it further through 45⁰ is?

Q.

a satellite revolves round a planet in a circular orbit of radius r. if the gravitational force on the satellite by the planet is F newton, what is the work done by the planet on the satellite when the satellite covers half of orbit

Q. Time period of revolution of a planet depends on radius of the orbit are mass of sun (M) and universal gravity (G) prove dimensions that T square Alpha R cube ?

Q. A uniform rod of mass $5\text{kg}$ and length $3\text{m}$ is held at an angle $\theta ={37}^{\circ }$ with the horizontal as shown in the figure. The potential energy of the rod is (in $\text{J}$)

1. $\frac{21g}{2}$
2. $\frac{9g}{2}$
3. $12g$
4. $6g$