Potential Energy Formulae

Q. The mass of a bucket full of water is 15kg.It is being pulled up from a 15m deep well.Due to a hole in the bucket 6kg water flows out of the bucket.The work done in drawing the bucket out of the well will be(g=10m/s2)

Q. A man pulls a bucket full ofwater from h metre deep well. if the mass of rope is m and mass of bucket full of water is M, then work done by the man is

Q. The mass of the a bucket full of water is 15kg. It is being pulled up from a 15m deep well. Due to the hole in the bucket 6kg water flows out of the bucket. The work done in drawing the bucket out of the water will be:- (1)900J (2)1500J (3)1800J (4)2100J

Q.

A vertical mass-spring system executes simple harmonic oscillations with a period of 2 s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is

1. Velocity

2. Potential energy

3. Phase difference between acceleration and displacement

4. Difference between kinetic energy and potential energy

Q.

When does the potential energy of a spring increase?

Q. A particle of mass $2\text{kg}$ executes simple harmonic motion and its potential energy $U$ varies with position $x$ as shown below. The period of oscillation of the particle is

1. $\frac{2\pi }{5}\text{s}$
2. $\frac{2\sqrt{2}\pi }{5}\text{s}$
3. $\frac{\sqrt{2}\pi }{5}\text{s}$
4. $\frac{4\pi }{5}\text{s}$

Q. A cylindrical tube open at both the ends has a fundamentaf requency of 390 Hz in air. If 1/4 -th of the tube is immersed vertically in water the fundamental frequency of air column is

Q. a man pull a bucket full of water from h metre deep well. if the mass of rope is m and mass of bucket full of water is M , tgen work done by the man is

Q. A cubical vessel of height 1m is full of water. The minimum work done in taking water out from vessel will be }1) 5000 J 2) 10000J 3)5J 4)10J

Q. The potential energy of a particle executing simple harmonic motion at a distance x from the equilibrium position is proportional to

1. $\sqrt{x}$
2. $x$
3. $x^2$
4. $x^3$

Q.

A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U(x) = k $[x{]}^3$ , where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

1. Proportional to

2. Proportional to

3. Proportional to

4. Independent of a

Q. Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

Q. The potential energy of the spring increases times, when the elongation of the spring is doubled.

1. two
2. three
3. four

Q. A linear simple harmonic oscillation has a total mechanical energy of $300\text{J}$. Its potential energy at mean position is $100\text{J}$. Find the minimum potential energy.

1. $50\text{J}$
2. $250\text{J}$
3. $100\text{J}$
4. $200\text{J}$

Q. A body is executing simple harmonic motion. At a displacement x, its potential energy is $E_1$ and at a displacement y, its potential energy is$E_2$ The potential energy E at a displacement $(x+y)$ is

1. $E_1+E_2$
2. $\sqrt{E_1^2+E_2^2}$
3. $E_1+E_2+2\sqrt{E_1{E}_2}$
4. $\sqrt{E_1{E}_2}$

Q. In the equation $x=A\sin (\omega t+\frac{\pi }{4})$. Match the following, when $x=\frac{A}{2}$

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) Kinetic energy}& \text{(p) Half the maximum value}\\ \text{(B) Potential energy}& \text{(q) 3/4 times the maximum value}\\ \text{(C) Acceleration}& \text{(r) 1/4 times the maximum value}\\ & \text{(s) Cannot say anything}\end{array}$

1. $A\to q,B\to p,C\to s$
2. $A\to q,B\to s,C\to p$
3. $A\to q,B\to p,C\to s$
4. $A\to q,B\to s,C\to s$

Q. A linear simple harmonic oscillation has a total energy of $250\text{J}$. If the potential energy at mean position is $50\text{J}$, then find the maximum kinetic energy.

1. $50\text{J}$
2. $200\text{J}$
3. $100\text{J}$
4. $150\text{J}$

Q.

A ice block floating in a river is pushed through a displacment d=(15m) - (12m) alon] a staight A embankment by rushing water , which exerts a force F=(210N) - (150N) on the block . how much work does the force do on the block during the displacement ?

Q. Conditions for node and antinode

Q. The variation of PE of harmonic oscillator is as shown in figure. The spring constant is

1. $1\times {10}^2{\text{Nm}}^{-1}$
2. $1.5\times {10}^2{\text{Nm}}^{-1}$
3. $2\times {10}^2{\text{Nm}}^{-1}$
4. $3\times {10}^2{\text{Nm}}^{-1}$

Q.

A particle oscillates about the equilibrium position $x_0$ subject to a force that has an associated potential energy U(x). Which of the following statements about U(x) is/are true:

1. u(x) must be symmetric about x${}_0$
2. u(x) must have a minimum at x${}_0$
3. u(x) may have a minimum at x${}_0$
4. u(x) must be positive in the vicinity of x${}_0$

Q. A cubical vessel of height 1m is full of water. The minimum work done in taking water- out from vessel will be

Q. a man pulls a bucket full of water from h metre well. If the mass of rope is m and mass of bucket full of water is M , then the work done by the man is 1) (M/2+m)gh 2) (M+m)/2 3) (M+m/2)gh 4) (M+m)gh