Time Period of Pendulum

Q.

The length of a simple pendulum is increased by 1%. Its time period will

1. increase by 1%

2. increase by 0.5%

3. decrease by 0.5%

4. increase by 2%.

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. If the mass of the object in a spring-mass system is increased by 4 times then the time period will be doubled.

1. False
2. True

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. A simple pendulum $50\text{cm}$ long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration of $\sqrt{3}g{\text{m/s}}^2$. The period of small oscillations of the pendulum about its equilibrium position is -
$(g={\pi }^2{\text{m/s}}^2)$

1. $1.0\text{sec}$
2. $\sqrt{2}\text{sec}$
3. $1.53\text{sec}$
4. $1.68\text{sec}$

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. If the length of second's pendulum is decreased by $2\%$, how many seconds it will loose per day ?

1. $3927\text{s}$
2. $3727\text{s}$
3. $3427\text{s}$
4. $864\text{s}$

Q. A simple pendulum of length $l$ is suspended from the ceiling of a trolley which is moving, without friction, down an inclined plane of inclination . 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 sin $\theta$
3. g cos $\theta$
4. g tan $\theta$

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

1. 
2. 
3. 
4. 

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

1. $10\%$
2. $20\%$
3. $40\%$
4. $44\%$

Q. What are the two types of longitudinal stresses?

1. Tensile stress and compressive stress
2. Compressive stress and normal stress
3. Normal stress and sheer stress
4. Shear stress and tensile stress

Q. A pendulum clock consists of a $1\text{m}$ rod connected to a small, heavy bob. If it is designed to keep correct time at ${30}^{\circ }\text{C}$, how fast or slow will it go in 12 hours at ${50}^{\circ }\text{C}$? Coefficient of linear expansion of iron $=1.2\times {10}^{-5}{/}^{\circ }\text{C}$.

1. $5.2\text{sec}$, slow
2. $5.2\text{sec}$, fast
3. $4\text{sec},$ fast
4. $4\text{sec},\text{slow}$

Q. If the length of second's pendulum is decreased by $2\%$, how many seconds it will loose per day ?

1. $3927\text{s}$
2. $3727\text{s}$
3. $3427\text{s}$
4. $864\text{s}$

Q. A simple pendulum has a time period $T$ in vaccum. Its time period when it is completely immersed in a liquid of density one-eight of the density of material of the bob is

1. $\sqrt{\frac{7}{9}}T$
2. $\sqrt{\frac{5}{8}}T$
3. $\sqrt{\frac{3}{8}}T$
4. $\sqrt{\frac{8}{7}}T$

Q. Two simple pendulums whose lengths are $100\text{cm}$ and $121\text{cm}$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum, will the two be in phase again.

1. $11$
2. $10$
3. $21$
4. $20$

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. $32\text{cm}$

Q. The length of a simple pendulum executing simple harmonic motion is increased by $10\%$. The percentage increase in the time period of the pendulum due to increased length will be:

1. $10\%$
2. $5\%$
3. $15\%$
4. $20\%$

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. 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 out
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. 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. $1\text{rad/s}$
4. $0.1\text{rad/s}$

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

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. $32\text{cm}$

Q. A small bob attached to a light inextensible thread of length $l$ has a periodic time $T$ when allowed to vibrate as a simple pendulum. The thread is now suspended from a fixed end O of a vertical rigid rod of length $\frac{3l}{4}$ (as in figure.) If now the pendulum performs periodic oscillations in this arrangement, the periodic time will be

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

Q. Two blocks $A$ and $B$ of mass $m$ and $2m$ are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. Spring is stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is

1. $\left(\sqrt{\frac{3k}{2m}}\right)x$
2. $\left(\sqrt{\frac{2k}{3m}}\right)x$
3. $\sqrt{\frac{2kx}{m}}$
4. $\sqrt{\frac{3km}{2x}}$

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 seconds pendulum is decreased by 2%, How many seconds it will lose per day?

1. 3927 sec

2. 3727 sec

3. 3427 sec

4. 864 sec

Q. If a simple pendulum has point of suspension at rest, the period of oscillation $T$ is related to length of the pendulum $l$ as:

1. $\frac{l}{T}=\text{constant}$
2. $\frac{l^2}{T}=\text{constant}$
3. $\frac{l}{T^2}=\text{constant}$
4. $\frac{l^2}{T^2}=\text{constant}$

Q. Two blocks $A$ and $B$ of mass $m$ and $2m$ are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. Spring is stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is

1. $\left(\sqrt{\frac{3k}{2m}}\right)x$
2. $\left(\sqrt{\frac{2k}{3m}}\right)x$
3. $\sqrt{\frac{2kx}{m}}$
4. $\sqrt{\frac{3km}{2x}}$