Kinetic Energy Formulae

Q.

A loaded vertical spring executes simple harmonic oscillations with period of 4 s. The difference between the kinetic energy and potential energy of this system oscillates with a period of

1. 1 s

2. 4 s

3. 8 s

4. 2 s

Q. Energy of particle executing $\text{SHM}$ depends upon

1. Amplitude only
2. Amplitude and frequency
3. Velocity only
4. Frequency only

Q. If particle is executing simple harmonic motion with time period T, then the time period of its total mechanical energy is (1) Zero(2)T/2(3) 2T (4) Infinite

Q. A particle of mass m executes simple harmonic motion with amplitude a and frequency_v. The average kinetic energy during its motion fromthe position of equilibrium to the end is

Q. in a certain field the potential energy is u=ax^2-bx^3 where a and b are cons†an t the particle is in stable equilibrium at x is equals to

Q. In a SHM, potential energy of a particle at mean position is $E_1$ and kinetic energy is $E_2,$ then

1. $E_1=E_2$
2. $\text{total potential energy at}x=\frac{\sqrt{3}A}{2}\text{is}{E}_1+\frac{3}{4}{E}_2$
3. $\text{total potential energy at}x=\frac{\sqrt{3}A}{2}\text{is}\frac{3}{4}{E}_2$
4. $\text{None of these}$

Q.

A particle executes a SHM with frequency $\nu$. The frequency of variation of potential energy will be :

1. v

2. 2v

3. v/2

4. 3 $\nu$

Q. 46.A particle is undergoing SHM has the equation x= A sin (wt + Q(fi) ) where x represents the displacement of the particle. The kinetic energy oscillates with time period

Q.

Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring in its natural length, as shown in figure.

A third identical block C, also of mass m moves on the floor with a speed v along the line joining A and B collides with A, elastically. Then,

1. The kinetic energy of the AB system at maximum compression of the spring is mv².

2. The maximum compression of the spring is.

3. The maximum compression of the spring is.

4. The kinetic energy of AB system at maximum compression of the spring is zero.

Q. A particle of mass $0.3\text{kg}$ executes SHM with an amplitude $0.06\text{m}$ and frequency $10$ vibrations/sec. Find its total energy of oscillation.

1. $5\text{J}$
2. $2.13\text{J}$
3. $3\text{J}$
4. $8.5\text{J}$

Q. 69.A block of mass m with a spring attached is resting on smooth horizontal floor. Velocity v is given to the other free end of spring. Find the maximum energy of the system during subsequent motion.

Q. A body of mass 1 kg is executing simple harmonic motion. Its displacement x (in cm) at time t (in second) is given by
$x=6sin(100t+\frac{\pi }{4})$The maximum kinetic energy of the body is

1. 6 J
2. 18 J
3. 24 J
4. 36 J

Q. A body of mass 5 kg is moving with a momentum of 10 kg m/s. A force of 0.2 N acts on it in the directionof motion of the body for 10 s. The increase in its kinetic energy is

Q. 22. The kinetic energy acquired by a body of mass `m is travelling some distance s starting form rest under the action of a constant force is directly proportional to Options: m0 m m2

Q. A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is
(a) v/2
(b) v
(c) 2 v
(d) zero

Q.

A particle executes a SHM with frequency $\nu$. The frequency of variation of potential energy will be :

1. 2 $\nu$

2. $\nu$

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

4. 3 $\nu$

Q.

A particle executes S.H.M (a) What fraction of total energy is kinetic? What fraction is potential when displacement is one half of the amplitude?

1. $\frac{3}{4}$ and $\frac{1}{4}$

2. $\frac{2}{3}$ and $\frac{1}{3}$

3. $\frac{1}{2}$ and $\frac{1}{2}$

4. $\frac{1}{6}$ and $\frac{5}{6}$

Q. Assertion: Average kinetic energy in one oscillation during $\text{SHM}$ of a body is $\frac{1}{4}m{\omega }^2{A}^2$.
Reason: Maximum kinetic energy is $\frac{1}{2}m{\omega }^2{A}^2$.

1. If both assertion and reason are correct and reason is the correct explanation of assertion.
2. If both assertion and reason are correct but reason is not the correct explanation of assertion.
3. Assertion is true but reason is false.
4. Assertion is false but reason is true.

Q. Energy of particle executing $\text{SHM}$ depends upon

1. Amplitude only
2. Amplitude and frequency
3. Velocity only
4. Frequency only

Q. A particle of mass m is executing oscillation about the origin on the x axis. Its potential energy is U=K|x|^3 where k is positive constant. If the amplitude of oscillation is a, then its time period T is

Q. A spring stretches by 0.05 m when a mass of 0.5 kg is hung from it. A body of mass 1.0 kg is attached to one of its ends, the other end being fixed to the wall. The body is pulled 0.01 m along a horizontal frictionless surface and released. What is the total energy of the oscillator. Assume the string to have negligible mass and take $g=10m{s}^{-2}$

1. 0.005 J
2. 0.05 J
3. 0.5 J
4. 5 J

Q. What is mechanical energy for a body having escape velocity. Explain

Q. Two blocks A and B each of mass $m$ are connected by a massless spring of natural length $L$ and spring constant $k$. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in figure. A third identical block C, also of mass $m$ moves on the floor with a speed $v$ along the line joining A and B. C collides with A elastically. Then:

1. The kinetic energy of AB system at maximum compression of the spring is zero.
2. The kinetic energy of the AB system at maximum compression of the spring is $\frac{m{v}^2}{4}$.
3. The maximum compression of the spring is $v\sqrt{\frac{m}{k}}$.
4. The maximum compression of the spring is $v\sqrt{\frac{m}{2k}}$.

Q. A particle of mass $400\text{g}$ is executing SHM of amplitude $0.4\text{m}$. When it passes through the mean position, its kinetic energy is $32\times {10}^{-3}\text{J}$. If the initial phase of oscillation is $\frac{\pi }{4}$, then the equation of motion of the particle is

1. $0.4\sin (2t+\frac{\pi }{4})$
2. $0.4\cos (2t+\frac{\pi }{4})$
3. $0.4\sin (t+\frac{\pi }{4})$
4. $0.4\cos (t+\frac{\pi }{4})$

Q.

A particle executes a SHM with frequency $\nu$. The frequency of variation of potential energy will be :

1. 2 $\nu$

2. $\nu$

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

4. 3 $\nu$

Q. If the initial potential energy is zero, the energy at the mean position $(x=0)$ of simple harmonic oscillation will be

1. Zero
2. Partial PE and partial KE
3. Totally KE
4. Totally PE

Q. Total energy of a particle having a displacement ${}^{\prime }{x}^{\prime }$ executing simple harmonic motion is

1. proportional to $x$
2. proportional to $x^2$
3. Independent of $x$
4. proportional to $x^{1/2}$

Q. A constant force P is applied to a car starting from rest. Then if in time t the car travel a distance x, its kinetic energy is proportional to

Q. A particle performs S.H.M of amplitude $A$ along a straight line. When it is at a distance $\frac{\sqrt{3}A}{2}$ from mean position, its kinetic energy gets increased by an amount $\frac{1}{2}m{\omega }^2{A}^2$ due to an impulsive force. Then its new amplitude becomes $nA$. Find $n$:

Q. The total vibrational energy of a particle in $\text{SHM}$ is $E$. Its kinetic energy at half the amplitude from mean position will be :

1. $E/2$
2. $E/3$
3. $E/4$
4. $3E/4$