If the length of second pendulum becomes $\frac{1}{3}$ what will be its periodic time ?
If the length of second pendulum becomes $\frac{1}{3}$ what will be its periodic time ?
$\frac{2}{\sqrt{3}} \mathrm{~s}$
Time period of second pendulum $T_{1}=2 s$
In equation $\mathrm{T}=2 \pi \sqrt{\frac{l}{g}}, 2 \pi, g$ are constant
$\therefore \quad \mathrm{T} \propto \sqrt{l}$
$\therefore \quad \frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\sqrt{\frac{l_{2}}{l_{1}}}=\sqrt{\frac{l_{1}}{3 \times l_{1}}}=\frac{1}{\sqrt{3}} \quad\left[\because l_{2}=\frac{l_{1}}{3}\right]$
$\therefore \quad \mathrm{T}_{2}=\frac{\mathrm{T}_{1}}{\sqrt{3}}=\frac{2}{\sqrt{3}} \mathrm{~s}$
Similar Questions
A bob of mass $'m'$ suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period ${T}$. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the thread is increased by $1 / 3^{\text {rd }}$ of the original length, then the time period of the simple harmonic oscillations will be :-
A bob of mass $'m'$ suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period ${T}$. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the thread is increased by $1 / 3^{\text {rd }}$ of the original length, then the time period of the simple harmonic oscillations will be :-
- [JEE MAIN 2021]
The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height h above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\, sec$, the tension in the string when the bob passes through $O$ is
The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height h above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\, sec$, the tension in the string when the bob passes through $O$ is
Can simple pendulum clock be used in an artificial satellite ? Why ?
Can simple pendulum clock be used in an artificial satellite ? Why ?
Choose the correct length $( L )$ versus square of time period $\left( T ^2\right)$ graph for a simple pendulum executing simple harmonic motion.
Choose the correct length $( L )$ versus square of time period $\left( T ^2\right)$ graph for a simple pendulum executing simple harmonic motion.
- [JEE MAIN 2023]
A simple pendulum, suspended from the ceiling of a stationary van, has time period $T$. If the van starts moving with a uniform velocity the period of the pendulum will be
A simple pendulum, suspended from the ceiling of a stationary van, has time period $T$. If the van starts moving with a uniform velocity the period of the pendulum will be