A simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration, the frequency of the simple pendulum will
Increase
Decrease
Become infinite
Remain constant
If the mass of a bob of a pendulum increased by $9$ times, the period of pendulum will ?
Column $I$ gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column $II$. Match the set of parameters given in Column $I$ with the graph given in Column $II$. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the $ORS$.
Column $I$ | Column $II$ |
$(A)$ Potential energy of a simple pendulum (y axis) as a function of displacement ( $\mathrm{x}$ axis) | $Image$ |
$(B)$ Displacement (y axis) as a function of time (x axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive $\mathrm{x}$-direction | $Image$ |
$(C)$ Range of a projectile (y axis) as a function of its velocity ( $\mathrm{x}$ axis) when projected at a fixed angle | $Image$ |
$(D)$ The square of the time period (y axis) of a simple pendulum as a function of its length ( $\mathrm{x}$ axis) | $Image$ |
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 pendulum bob has a speed of $3\, m/s$ at its lowest position. The pendulum is $0.5\, m$ long. The speed of the bob, when the length makes an angle of ${60^o}$ to the vertical, will be ..... $m/s$ (If $g = 10\,m/{s^2}$)
A pendulum suspended from the ceiling of a train has a period $T$, when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation will