COE in SHM

Q.

Convert $1\mathrm{joule}$ to $\mathrm{ergs}$ in dimensional analysis.

Q.

Time period of a simple pendulum measured inside a stationary lift is T. If the lift starts moving upwards with an acceleration of $\frac{g}{3}$, what will be its time period:

1. $3T$

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

3. $\frac{\sqrt{3}}{2T}$

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

Q.

Taking force, length and time to be the fundamental quantities find the dimensions of

(a) density,

(b) pressure,

(c) momentun and

(d) energy.

Q.

A body of mass $5gm$ is executing S.H.M. about a point with amplitude $10cm$. Its maximum velocity is $100cm/s$. Then, the velocity of body will be $50cm/s$ at a distance of (in $cm$)

1. 10$\sqrt{2}$
2. 5$\sqrt{3}$
3. 5$\sqrt{2}$
4. 5

Q. A particle executes SHM with time period $T$ and amplitude $A$. The maximum possible average velocity in time $\frac{T}{4}$ is:

1. $\frac{2A}{T}$
2. $\frac{4A}{T}$
3. $\frac{8A}{T}$
4. $\frac{4\sqrt{2}A}{T}$

Q.

A transformer ia used to light a 100W and 110V lamp from a 220V mains. If the main current is 0.5amp , the efficiency of the transformer is approx

1)10%

2)30%

3)50%

4)90%

Q. A $12\text{V}$ battery connected to a bulb drives a current of $2\text{A}$ through it. Find the energy supplied by the battery in $10\text{minutes}$.

1. $12.4\text{kJ}$
2. $13.4\text{kJ}$
3. $15.4\text{kJ}$
4. $14.4\text{kJ}$

Q. Q. A spring with spring constant k when compressed by 1 cm, the potential energy stored is U. if it is further compressed by 3 cm then change in potential energy is
3U
9U
8U
15U

Q. The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $\left(\frac{4}{3}\right)\times 1000kg/m^3$. What relationship between t and $t_0$is true

1. t=t_o
2. t=t_o/2
3. t=2t_o
4. t=4t_o

Q.

For what value of displacement do the kinetic energy and potential energy of a simple harmonic oscillation become equal?

1. $x=\frac{A}{2}$

2. $x=0$

3. $x=\pm A$

4. $x=\pm \frac{A}{\sqrt{2}}$

Q.

A particle undergoing simple harmonic motion has time-dependent displacement given by $x\left(t\right)=Asin\frac{\pi t}{90}$. The ratio of kinetic to the potential energy of this particle at $t=210s$ will be

1. $1$

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

3. $\frac{1}{9}$

4. $2$

Q.

Dimensional formula for amplitude of vibration

Q. Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocities of blocks (in m/s) in case of maximum compression are

1. 5, 5
2. 10, 10
3. 8, 4
4. 7, 7

Q. 11. A monochromatic point source of light is placedat a distance d from a metal surface. Photoelectrons are ejected at a rate n per second, andwith maximum kinetic energy E. If the source isbrought nearer to distance d/2, the rate and themaximum kinetic energy per photoelectronbecome nearly(1) 2n and 2E(2) 4n and 4E(3) 4n and E(4) n and 4E why the energy is not changing bcoz of rate become 4 times then frequency will also become 4tims

Q. In a simple harmonic oscillator, at the mean position

1. Kinetic energy is minimum, potential energy is maximum
2. Both kinetic and potential energies are maximum
3. Kinetic energy is maximum, potential energy is minimum
4. Both kinetic and potential energies are minimum

Q. Find the time period of mass $M$ when displaced from its equilibrium position and then released for the system shown in Figure.

Q. A block $\left(B\right)$ is attached to two unstretched springs $S_1$ and $S_2$ with spring constant $2k$ 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 and the surface is frictionless. The block $B$ is displaced towards wall $1$ by a small distance $x$ and released. The block returns and moves a maximum distance $y$ towards wall $2$. Displacement $x$ and $y$ is measured with respect to the equilibrium position of the block $B$. The ratio of $\frac{y}{x}$ is

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

Q.

A particle executing simple harmonic motion with an amplitude A.The distance travelled by the particle in one time period is

A)zero B)A C)2A D)4A

Q.

A boy moves 6 m towards east and then 8 m towards north .Calculate the distance and displacement .

Q.

A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant $100N{m}^{-1.}$ A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, find the frequency and the amplitude of the motion.

Q. The total energy of a harmonic oscillator of mass $2\text{kg}$ is $9\text{J}$. If its potential energy at mean position is $5\text{J}$, its $\text{K.E.}$ at the mean position will be :

1. $14\text{J}$
2. $4\text{J}$
3. $11\text{J}$
4. $9\text{J}$

Q.

A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle θ with the vertical

1. in the backward direction

2. in the backward direction

3. in the forward direction

4. in the forward direction

Q.

Two copper circular discs are of the same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is

1. 8 times as large

2. 16 times as large

3. Four times as large

4. Twice as large

Q.

Two blocks of masses 400 g and 200 g are connected through a light string going over a pulley which is free to rotate about its axis. The pulley has a moment of inertia 1.6 $\times {10}^{-4}$ ${\text{kg-m}}^2$ and a radius 2.0 cm. Find (a) the kinetic energy of the system as the 400 g block falls through 50 cm, (b) the speed of the blocks at this instant.

Q. A particle is performing SHM. When the displacement is one half of its amplitude, find what fraction of total energy are the kinetic and potential energies of the particle?

1. $\frac{3}{4},\frac{1}{4}$
2. $\frac{3}{8},\frac{5}{8}$
3. $\frac{1}{3},\frac{2}{3}$
4. $\frac{2}{3},\frac{1}{3}$

Q. when a voltage V equal to vo cos WT is applied across a resistor of resistance are the average power dissipated per cycle in the resistor is given by

Q. In simple harmonic motion:

1. Potential energy and kinetic energy may not be equal in mean position.
2. Potential energy and kinetic energy may be equal in extreme position.
3. Potential energy may be zero at extreme position.
4. Kinetic energy plus potential energy oscillates simple harmonically.

Q.

Does a compressed spring have kinetic energy$?$

Q. Why does a simple pendulum eventually stop?

Q.

A vehicle is moving on a straight horizontal road at a constant velocity of $10m{s}^{-1}$. The engine needs to spend $4kJ$ of energy per second. The force on the vehicle is

1. $0.2kN$

2. $0.4kN$

3. $0.6kN$

4. $1N$