Intro to Simple 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. Decrease
2. Increase
3. Remains unchanged
4. Become erratic

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

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

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

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. 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. The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down in an inclined plane of inclination α, is given by

1. $2\pi \sqrt{\frac{L}{gcos\alpha }}$
   
2. $2\pi \sqrt{\frac{L}{gsin\alpha }}$
   
3. $2\pi \sqrt{\frac{L}{g}}$
   
4. $2\pi \sqrt{\frac{L}{gtan\alpha }}$

Q. A pendulum executes SHM. The acceleration of the bob of pendulum is ${\pi }^2{\text{m/s}}^2$ at a distance of $2\text{m}$ from the mean position. Find the time period of oscillation.

1. $2\text{seconds}$
2. $\sqrt{2}\text{seconds}$
3. $2\sqrt{2}\text{seconds}$
4. $\sqrt{2}{\pi }^2\text{seconds}$

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. 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 has a time period of 3.0 s. If the point of suspension of the pendulum starts moving vertically upward with a velocity v = kt where $k=4.4m{s}^{-2}$, the new time period will be (Take g = 10 $m{s}^{-2}$

1. $\frac{9}{4}s$
   

2. $\frac{5}{3}s$
   

3. $2.5s$
   

4. $4.4s$