Intro to Simple Pendulum

Q. The length of a simple pendulum is $\frac{39.2}{{\pi }^2}\text{m}$. If $g=9.8{\text{m/s}}^2$, the time period of pendulum is

1. $2\text{s}$
2. $8\text{s}$
3. $4\text{s}$
4. $3\text{s}$

Q.

A simple pendulum attached to the ceiling of a stationary lift has a time period T. The distance y covered by the lift moving upwards varies with time t as $y=t^2$ where y is in metre and t in second. If $g=10m{s}^{-2}$, the time period of the pendulum will be

1. $\sqrt{\frac{4}{5}}T$

2. $\sqrt{\frac{5}{6}}T$

3. $\sqrt{\frac{5}{4}}T$

4. $\sqrt{\frac{6}{5}}T$

Q. A small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is $T_0$. When parallel plates are charged, the time period changes to T. The ratio $\frac{T}{T_0}$ is equal to

1. None of these
2. ${\left(\frac{g+\frac{qE}{m}}{g}\right)}^{1/2}$
3. ${\left(\frac{g}{g+\frac{qE}{m}}\right)}^{3/2}$
4. ${\left(\frac{g}{g+\frac{qE}{m}}\right)}^{1/2}$

Q. In a uniform magnetic field, the magnetic needle has a magnetic moment $9.85\times {10}^{–2}{\text{A/m}}^2$ and moment of inertia $5\times {10}^{–6}{\text{kg m}}^2$. If it performs $10$ complete oscillations in $5\text{seconds}$ then the magnitude of the magnetic field is $\text{mT}$.
[Take ${\pi }^2$ as $9.85$]

Q.

The length of the second’s pendulum on the surface of earth is 1m. The length of second’s pendulum on the surface of moon, where g is $\frac{1}{6}th$ value of earth surface, is:

1. $\frac{1}{6}m$

2. $\frac{1}{36}m$

3. $6m$

4. $36m$

Q. Find the time period of torsional pendulum.

Q.

Does air resistance affect the period of a pendulum$?$

Q. A simple pendulum is made of a body which is a hollow sphere containing mercury, suspended by means of a wire. If a little mercury is drained off, then the time period of pendulum

1. Increase
2. Remains unchanged
3. Decrease
4. Become erratic

Q.

A simple pendulum makes $10$ oscillations in $20$ seconds. What is the time period and frequency of its oscillation?

Q.

How do you double the period of a pendulum?

Q. If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will

1. Decrease
2. Increase
3. Remain the same
4. May increase or decrease

Q. Why does the pendulum stop after oscillating for a while?

Q. A bob of a simple pendulum of mass 40gm with a positive charge $4\times {10}^{-6}$ is oscillating with time period ‘$T_1$’. An electric field of intensity $3.6\times {10}^4$ N/c is applied vertically upwards now time period is $T_2$. The value of $\frac{{}^{\prime }{T}_2^{\prime }}{T_1}$ is (g = 10 $m/s^2$)

1. 0.16
2. 0.64
3. 1.25
4. 0.8

Q. A pendulum clock of time period $2\text{sec}$ gives the correct time at ${30}^{\circ }\text{C}$. The pendulum is made of iron. How many seconds will it lose or gain per day when the temperature falls to $0^{\circ }\text{C}$ ? ${\alpha }_{Fe}=1.2\times {10}^{-5}{(}^{\circ }\text{C}{)}^{-1}$

1. $15.5\text{sec}$
2. $20.5\text{sec}$
3. $30.5\text{sec}$
4. No gain/loss.

Q. Magnets A and B are geometrically similar but the magnetic moment of A is twice that of B. If $T_1$ and $T_2$ are the time periods of oscillation when their like poles and unlike poles are kept together respectively, then $\frac{T_1}{T_2}$ will be -

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

Q.

Why do shorter pendulums swing faster?

Q.

Length of a seconds pendulum is approximately:

1. 9.9 cm

2. 99.9 cm

3. 99 cm

4. 999 cm

Q. A simple pendulum with a brass bob has a time period T. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $\frac{1}{8}$ that of brass, the time period of the same pendulum will be

1. $\sqrt{\frac{8}{7}}T$
2. $\frac{8^2}{7^2}T$
3. $T$
4. $\frac{8}{7}T$

Q. When will the motion of a simple pendulum be simple harmonic?

Q.

A particle of mass $0.1kg$ executes SHM under a force $F=(-10x)N$. Speed of particle at mean position is $6m/s.$Then amplitude of oscillations is

1. $0.6m$

2. $0.2m$

3. $0.4m$

4. $0.1m$

Q. A simple pendulum of bob mass m is oscillating with an angular amplitude ${\alpha }_m$ (in radian). The maximum tension in the string is

1. $mg{\alpha }_m^2$
2. $mg$
3. $mg{\alpha }_m$
4. $mg(1+{\alpha }_m^2)$

Q. The bob of simple pendulum having density $\frac{4000}{3}{\text{kg/m}}^3$ executes $\text{SHM}$ in water with a period ${}^{\prime }{t}^{\prime }\text{s}$. If the period of oscillation of bob in air is $10\text{s}$, find the value of ${}^{\prime }{t}^{\prime }$.
(Neglect frictional force of water, take density of water as $1000{\text{kg/m}}^3$)

1. $10$
2. $20$
3. $30$
4. $40$

Q.

For small oscillations, a pendulum of length L is released from rest. Its length is L and time period is T. vertically below the point of suspension O, there is an obstacle P at a vertical distance x. the pendulum returns back to its original position after time $\frac{5T}{8}$. Find x.

1. L/2

2. 13L/16

3. 15L/16

4. 3L/4

Q.

In simple harmonic motion, motion is executed by a particle that is subject to a force which is ________ to the displacement of the particle and is directed toward the _________.

Q. Two pendulums whose lengths differ by $11\text{cm}$ oscillate at the same place so that one of them makes $30$ oscillations and the other $36$ oscillations during same time. Find the lengths of the pendulum.

1. $37\text{cm}\text{and}26\text{cm}$
2. $25\text{cm}\text{and}14\text{cm}$
3. $30\text{cm}\text{and}19\text{cm}$
4. $36\text{cm}\text{and}25\text{cm}$

Q. A simple pendulum completes 40 oscillations in a minute. Find its frequency.

Q. A girl is swinging in a swing in a sitting position. How will the period of the swing be affected if she stands up?

Q.

How many vibrations, a simple pendulum will complete in 52 second?

Q. A thin rectangular bar magnet suspended freely has a period of oscillation of $4\text{s}$. What will be the period of oscillation if the magnet is broken into two halves $($each having half the original length$)$ and one of the pieces is made to oscillate in the same field?

1. $2\text{s}$
2. $4\text{s}$
3. $6\text{s}$
4. $8\text{s}$

Q. A bar magnet is free to vibrate in a horizontal plane. At the magnetic equator, the time period of oscillations is found out to be equal to $T$. What will be its time period of oscillations on one of the magnetic poles of earth?

1. $T$
2. $\frac{T}{2}$
3. $2T$
4. infinity