Kinetic Energy Formulae

Q. A particle executes simple harmonic motion with a frequency. f. The frequency with which its kinetic energy oscillates is

1. 4f
2. 2f
3. f/2
4. f

Q.

A tuning fork $A$ of unknown frequency produces $5\frac{beats}{sec}$ with a fork of known frequency $340Hz$. When fork $A$ is filed, the beat frequency decreases to$2\frac{beats}{sec}$. What is the frequency of fork $A$?

1. $342Hz$

2. $335Hz$

3. $338Hz$

4. $345Hz$

Q.

What is the Hamiltonian operator in chemistry?

Q.

The equation of motion of a particle started at $t=0$ is given by $x=5$ sin $(20t+\frac{\pi }{3}),$ where x is in centimetre and t in second. When does the particle

(a) first come to rest

(b) first have zero acceleration

(c) first have maximum speed ?

Q.

Starting from the mean position a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy ?

1. (1/6)s

2. (1/3)s

3. (1/12)s

4. (1/4)s

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. A particle executes SHM, at what value of displacement are the kinetic and potential energies equal ?

1. $\sqrt{2}A$
2. $\frac{A}{\sqrt{2}}$
3. $\sqrt{\frac{3}{2}}A$
4. $\sqrt{\frac{2}{3}}A$

Q. In SHM, for how many times potential energy is equal to kinetic energy during one complete period?

1. $1$
2. $2$
3. $3$
4. $4$

Q.

A particle of mass 200 gm executes S.H.M. The restoring force is provided by a spring of force constant 80 N / m. The time period of oscillations is.

1. 0.31 sec

2. 0.15 sec

3. 0.05 sec

4. 0.02 sec

Q.

The time period of a particle executing SHM is $8sec$8 sec. At $T=0$, It Is at the mean position. Therefore, the ratio of the distance covered by the particle in the 1st second to the 2nd second is:

Q. A spring block system is put into $\text{SHM}$ in two experiments. In the first experiment, the block is pulled from the equilibrium position through a distance $d_1$ and then released. In the second experiment, it is pulled from the equilibrium position through a greater distance $d_2$ and then released. For the given scenario choose the incorrect statement.

1. Maximum kinetic energy is same for both $\text{SHM}$
2. Frequency is same for both $\text{SHM}$
3. Time period is same for both $\text{SHM}$
4. Angular frequency is same for both $\text{SHM}$

Q. A particle undergoing SHM has the equation $x=A\sin (\omega t+\varphi )$, where $x$ represents the displacement of the particle. The kinetic energy oscillates with time period

1. $\frac{2\pi }{\omega }$
2. $\frac{\pi }{\omega }$
3. $\frac{4\pi }{\omega }$
4. $\text{None of these}$

Q.

When a particle oscillates simple harmonically, its kinetic energies varies periodically.if frequency of the particle is f, the frequency of the kinetic energy is :

A)f/2 B)f C)2f D)4f

Q.

What is the kinetic energy of an electron?

Q. A particle is executing linear simple harmonic motion of amplitude A. What fraction of the total energy is kinetic when the displacement is half the amplitude?

1. $\frac{1}{4}$
2. $\frac{1}{2\sqrt{2}}$
3. $\frac{1}{2}$
4. $\frac{3}{4}$

Q. A body of mass $2\text{kg}$ is executing simple harmonic motion. Its displacement $y\text{(in cm)}$ at $t$ seconds is given by $y=6\sin (200t+\frac{\pi }{6})$. Find its maximum kinetic energy.

1. $144\text{kJ}$
2. $12\text{J}$
3. $48\text{kJ}$
4. $144\text{J}$

Q.

A dart is loaded into a spring-loaded toy dart gun by compressing the spring by a distance of $d$. For the next loading, the spring is compressed by a distance $2d$. How much faster does the second dart leave the gun compared to first?

1. Four times
2. Two times
3. Half times
4. One-fourth times

Q. Force constant of a weightless spring is $16\text{N/m}$. A body of mass $1.0\text{kg}$ suspended from it is pulled down through $5\text{cm}$ from its mean position and then released. The maximum kinetic energy of the body will be

1. $2\times {10}^{-2}\text{J}$
2. $4\times {10}^{-2}\text{J}$
3. $8\times {10}^{-2}\text{J}$
4. $16\times {10}^{-2}\text{J}$

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. 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. $E/4$
3. $E/3$
4. $3E/4$

Q.

A particle having mass 10 g oscillates according to the equation $x=\left(2.0cm\right)sin\left[100s^{-1}\right)t+\pi .6].$ Find (a) the amplitude, the time period and the spring constant (b) the position, the velocity and the acceleration at $t=0.$

Q.

The amplitude of a particle executing S.H.M. is $4\mathrm{cm}$. At the mean position, the speed of the particle is $16{\mathrm{cms}}^{-1}$. The distance of the particle from the mean position at which the speed of the particle becomes $8\sqrt{3}{\mathrm{cms}}^{-1}$, will be

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

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. $3\text{J}$
3. $8.5\text{J}$
4. $2.13\text{J}$

Q.

Raindrops of radius 1 mm and mass 4 mg are falling with a speed of 30 m/s on the head of a bald person. The drops splash on the head and come to rest. Assuming equivalently that the drops cover a distance equal to their radii on the head, estimate the force exerted by each drop on the head.

Q. A particle executes SHM of amplitude 25 cm and time periods 3 s. what is the minimum time required for the particle to move between two points located at 12.5 cm on either side of the mean position?

1. 0.25 s
2. 0.75 s
3. 1.0 s
4. 0.5 s

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

Q. Two bodies A and B of equal masses are suspended from two separate springs of force constants $k_{1}and{k}_2$ respectively. If the two bodies oscillate such that their maximum velocities are equal, the ratio of the amplitudes of oscillation of A and B will be

1. 
2. 
3. 
4. 

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. and

2. and

3. and

4. and

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. Totally KE
3. Totally PE
4. Partial PE and partial KE