Time Period of Pendulum

Q. A block of mass $m$ attached to a massless spring is performing oscillatory motion of amplitude $A$ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $fA$. The value of $f$ is:

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

Q. A seconds pendulum is moved to moon where acceleration due to gravity is $1/6$ times that of the earth, the length of the second pendulum on moon w.r.t length on earth would be:

1. $6\text{times}$
2. $12\text{times}$
3. $\frac{1}{6}\text{times}$
4. $\frac{1}{12}\text{times}$

Q. If the mass of the sun is made ten times smaller and the universal gravitational constant is made ten times larger in magnitude, then which of the following is not correct ?

1. Raindrops will fall faster.
2. $g$ on the earth will not change.
3. Time period of a simple pendulum on the earth would decrease.
4. Escape velocity of an object on the earth's surface will increase.

Q. Two pendulums have time period $T$ and $5T/4$. They start $\text{SHM}$ at the same time from the mean position. What will be the phase difference between them at the moment, when bigger pendulum completes one oscillation?

1. ${45}^{\circ }$
2. ${90}^{\circ }$
3. ${30}^{\circ }$
4. ${60}^{\circ }$

Q. The ratio of frequencies of oscillation for two simple pendulums are $2:3$, then their respective lengths are in ratio:

1. $\sqrt{\frac{2}{3}}:1$
2. $\sqrt{\frac{3}{2}}:1$
3. $9:4$
4. $4:9$

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. Two blocks of masses $m_1$ and $m_2$ are connected by a weightless spring of stiffness $k$, rests on a smooth horizontal plane. Mass $m_2$ is shifted by a small distance $x_0$ to the left and released. The velocity of the center of mass of the system when $m_1$ breaks off the wall is,

1. $\left(\frac{\sqrt{k{m}_2}}{m_1+m_2}\right)x_0$
2. $\left(\frac{\sqrt{k{x}_0{m}_2}}{m_1+m_2}\right)$
3. $\left(\frac{m_1+m_2}{m_2}\right)x_{0}k$
4. $\left(\frac{\sqrt{k{m}_1}}{m_1+m_2}\right)x_0$

Q. When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from $0.26\text{mm}$ to $0.13\text{mm}$. The ratio of the emissive powers of the body at the respective temperature is

1. $\frac{16}{1}$
2. $\frac{4}{1}$
3. $\frac{1}{4}$
4. $\frac{1}{16}$

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

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

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

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.

The pendulum of a certain clock has time period 2.04 s. How fast or slow does the clock run during 24 hours ?

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

1. 
2. 
3. 
4. 

Q. In a spring gun having spring constant $100\text{N/m}$, a small ball $B$ of mass $100\text{g}$ is put in its barrel (as shown in the figure) by compressing the spring through $0.05\text{m}$. There should be a box placed at a distance $d$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of $2\text{m}$ above the ground. The value of $d$ in meter is _______.

Take $g=10{\text{m/s}}^2$

Q. For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement $d$. Which one of the following represents these correctly?
(graphs are schematic and not drawn to scale)

1. 
2. 
3. 
4. 

Q. A clock with an iron pendulum keeps correct time at ${20}^{\circ }C$. How much will it lose or gain in 1 day if temperature changes to ${40}^{\circ }C$? [Given cubical expansion of iron $=36\times {10}^{-6}{}^{\circ }{C}^{-1}]$

1. 10.368 sec gain
2. 10.368 sec loss
3. 5.184 sec gain
4. 5.184 sec loss

Q.

A very broad elevator is going up vertically with a constant acceleration of $2m/s^2$. At the instant when its velocity is $4m/s$ a ball is projected from the floor of the lift with a speed of $4m/s$ relative to the floor at an elevation of ${30}^{\circ }$. The time taken by the ball to return the floor is ($g$ = $10m/s^2$) from time of projection.

1. 

2. 

3. 

4. 1 s

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

Q.

How does the time period of a swing change if a person sitting on it stands? What will happen if another person of same mass joins the first one?

Q. Can anyone please help me out with time dilation and how aging which is a biological clock gets affected with time dilation I mean how can it be that a person is of 70 years on earth whereas abother person on a space ship is of 50 at the same time

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 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 metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by

1. $T\frac{\rho -1}{\rho }$
2. $T\frac{\rho }{\rho -1}$
3. $T\sqrt{\frac{\rho -1}{\rho }}$
4. $T\sqrt{\frac{\rho }{\rho -1}}$

Q. The period of oscillation of a simple pendulum is T = $2\pi \sqrt{\frac{L}{g}}$. Measured value of L is 10 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 50 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g?

1. 2%
2. 3%
3. 4%
4. 5%

Q. A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles ${30}^{\circ }$ and ${60}^{\circ }$ from vertical (lowest position) are $T_1$ and $T_2$ respectively. Then

1. T₁ = T₂
2. T₂ > T₁
3. T₁ > T₂
4. Tension in the string always remains the same

Q.

If a simple pendulum is taken to a place where g decreases by 2%, then the time period

1. Increases by 1 %

2. Decreases by 1 %

3. Increases by 2 %

4. Decreases by 2 %

Q.

Why is SHM important?

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
3. g cos
4. g tan

Q.

Man measures the time period of a pendulum $\left(T\right)$ in a stationary lift. If the lift moves in an upward direction with an acceleration $\frac{g}{4}$, what will be the new time period?