Time Period of Pendulum

Q.

A simple pendulum with length L and mass M of the bob is vibrating with amplitude a. Then the maximum tension in the string is,

1. Mg

2. 

3. 

4. 

Q. The acceleration due to gravity on the surface of moon is 1.7 m s¯². What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s ? (g on the surface of earth is 9.8 m s¯²)

Q.

A seconds pendulum is placed in a space laboratory orbiting around the earth at a height 3R, where R is the radius of the earth. The time period of the pendulum is

1. Zero

2. 

3. 4 sec

4. Infinite

Q. 27.Water drops fall from the nozzle of a tap at height180 m. The drops fall at regular intervals of time. Thefirst drop strikes the floor at the instant when seventhdrop begins to fall. The time interval between twoconsecutive drops is (g 10 ms 2)6(1)S758(4)S(3) 1 s9UnoIr

Q. When the stretching force of a sonometer wire is increased by 2.5kg the frequency produced by it increases by 50% . Find the original stretching force.

Q. Consider the following data and choose the correct option.

$1.$ The time period of a simple pendulum, whose bob is a hollow metallic sphere is $T$.
$2.$ The time period of a simple pendulum is $T_1,$ when the bob is filled with sand,
$3.$ The time period of a simple pendulum is $T_2,$ when it is filled with mercury and
$4.$ The time period of a simple pendulum is $T_3,$ when it is half-filled with mercury as shown.

1. $T=T_1=T_2>T_3$
2. $T_1=T_1=T_3>T$
3. $T>T_3>T_1=T_2$
4. $T=T_1=T_2<T_3$

Q. 21.When the stretching force of a sonometer wire is increased by 2.5kg the frequency produced by it increases by 50% . Find the original stretching force.

Q. A simple pendulum of length l is suspended from the ceiling of a train which is moving in the horizontal direction with a constant acceleration a. The time period of the pendulum is given by $T=2\pi \sqrt{\frac{l}{g_{eff}}}$ where $g_{eff}$ is given by

1. g
2. (g+a)
3. (g- a)
4. $\sqrt{g^2+a^2}$

Q.

Two oscillating systems; a simple pendulum and a vertical spring - mass - system have same time period of motion on the surface of the Earth. If both are taken to the moon, then

1. Time period of the simple pendulum will be more than that of the spring - mass system

2. Time period of the simple pendulum will be equal to that of the spring - mass system

3. Time period of the simple pendulum will be less than that of the spring - mass system

4. Nothing can be said definitely without observation

Q.

The angle made by the string of a simple pendulum with the vertical depends on time as

$\theta =\frac{\pi }{90}sin\left[\right(\pi s^{-1}\left)t\right]$.Find the length of the pendulum if $g={\pi }^2\frac{m}{s^2}$.

1. $\pi m$

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

3. 1m

4. $\frac{90}{\pi }m$

Q. A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416. Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to
(a) 1 kg
(b) 2 kg
(c) 8 kg
(d) 16 kg.

Q. A clock with an iron pendulum keeps correct time at ${20}^{\circ }\text{C}$. If temperature is changed to ${40}^{\circ }\text{C}$, then which of the following is/are true?
[Take $\alpha =0.000012{/}^{\circ }\text{C}$]

1. Pendulum will gain $1.2\times {10}^{-4}$ seconds per each second.
2. Pendulum will lose $1.2\times {10}^{-4}$ seconds per each second.
3. Pendulum will gain $10.368$ seconds/day.
4. Pendulum will lose $10.368$ seconds/day.

Q. A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20m/s^2$ at a distance of $5m$ from the moving position. The time period of oscillation is

1. $2s$
2. $2\pi s$
3. $1s$
4. $\pi s$

Q. A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?

Q. Two pendula have time periods T and $\frac{5T}{4}$. They start SHM at the same time from the mean position. The phase difference between them after the pendulum with larger period completes one oscillation is

1. $\frac{\pi }{3}$
2. $\frac{\pi }{6}$
3. $\frac{\pi }{2}$
4. $\pi$

Q. In case of a simple pendulum, the time period versus length graph is correctly depicted by:

1. 
2. 
3. 
4. 

Q. A metal rod has a length of $1m$ at ${30}^{o}C$. $\alpha$ of metal is $2.5\times {10}^{-5}{/}^{o}C$. The temperature at which it will be shortened by $1mm$ is:

1. $-{30}^o$
2. $-{40}^o$
3. $-{10}^o$
4. ${10}^o$

Q. The time period of a simple pendulum is directly proportional to the square root of the.

1. length
2. mass
3. density

Q. The time period of simple pendulum changes when it is taken on the moon.

1. False
2. True

Q. Which of the following examples represent (nearly) simple harmonic motion and which represents periodic but not simple harmonic motion ?
(a) the rotation of earth about its axis.
(b) motion of an oscillating mercury column in a U-tube.
(c) motion of a ball bearing inside a smooth curved bowl when released from a point slightly above the lower most point.
(d) general vibrations of a poly-atomic molecule about its equilibrium position.

Q. A bob of simple pendulum is suspended by a thread of length $l=20\text{cm}$ , if it is placed in a liquid whose density is $\eta$ times less than that of the bob. If $\eta =3$, the time period of small oscillations is nearly equal to
Neglect the viscosity of liquid. Take $g=10{\text{m/s}}^2$

1. $1.1\text{s}$
2. $2\text{s}$
3. $3.1\text{s}$
4. $4.2\text{s}$

Q. 30 A simple pendulum with iron bob has a timeperiod T. The bob is now immersed in a non-viscous liquid and oscillated. If the density of liquidisth that of iron, then new time period will be1212(2) T12(4) T

Q.
Q. ​A simple pendulum oscillates, such that its amplitude is reduced to half of its initial amplitude $A_o$ at the end of 5 oscillations. What will be its amplitude after 10 complete oscillations?

Q. If at any time the displacement from mean position of a simple pendulum be $0.02\text{m}$, then its acceleration is $2{\text{m/s}}^2$. What is the angular frequency of the oscillation?

1. $100\text{rad/s}$
2. $10\text{rad/s}$
3. $0.1\text{rad/s}$
4. $1\text{rad/s}$

Q. A spherical ball of radius $5.5\text{cm}$ is oscillating in a hemispherical bowl. If the time taken to complete one oscillation by the ball is $\frac{\pi }{2}s$, then find the radius of hemispherical bowl.

1. $68\text{cm}$
2. $60\text{cm}$
3. $58\text{cm}$
4. $32\text{cm}$