Time Period of Pendulum

Q. Two simple pendulums $A$ and $B$ having length $l$ and $\frac{l}{4}$ respectively are released from the positions shown in the figure. If the time after release when the two strings become parallel for the first time is given by $\frac{2\pi }{x}\sqrt{\frac{l}{g}}\text{s}$, then the value of $x$ will be
[Assume angle $\theta$ is very small and motion starts at $t=0$]

Q.

If the length of a pendulum is made 9 times and mass of the bob is made 4 times then the value of time period becomes

1. 3T

2. 4T

3. 2T

4. 

Q.

Which of the following will change their time period as they are taken to moon?

1. A simple pendulum

2. A physical pendulum

3. A torsional pendulum

4. A spring-mass system

Q. A simple pendulum of frequency n is taken up to a certain height above the ground and then dropped along with its support so that it falls freely under gravity. The frequency of oscillations of the falling pendulum will

1. Remain equal to n
2. Become greater than n
3. Become less than n
4. Become zero

Q. A hollow metallic sphere filled with water is hung from a support by a long thread. A small hole is made at the bottom of the sphere and it is oscillated. How will the time period of oscillations be affected as water slowly flows out of the hole?

1. The time period will remain unchanged as water is flowing ou
2. The time period will keep increasing until the sphere is empty
3. The time period will keep decreasing until the sphere is empty
4. The time period will increases at first, then decrease until the sphere is empty; finally the period will be the same as that when the sphere was full of water.

Q.

The bob of a simple pendulum has a mass m and it is executing simple harmonic motion of amplitude A and period T. it collides with a body of mass $m_0$ placed at the equilibrium position which sticks to the bob. The time period of the oscillation of the combined masses will be

1. 
2. 
3. 
4. 

Q. A simple pendulum is moving simple harmonically with a period of 6 s between two extreme position B and C about a point O. If the angular distance between B and C is 10 cm, how long will the pendulum take to move from position C to a position D exactly midway between O and C

1. 3 s
2. 0.5 s
3. 1.0 s
4. 1.5 s

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. 

2. 

3. 1m

4. 

Q. The length of a simple pendulum is increased by $44\%$. What is the percentage increase in its time period?

1. 
2. 
3. 
4. 

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

1. T
2. 
3. 
4.