A weightless spring of length $60\, cm$ and force constant $200\, N/m$ is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of $0.25\, kg$ is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is
A$\frac{\pi }{{20}}s$
B$\frac{\pi }{{10}}s$
C$\frac{\pi }{5}s$
D$\frac{\pi }{{\sqrt {200} }}s$
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A$\frac{\pi }{{20}}s$
a (a) System is equivalent to parallel combination of springs
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A pendulum suspended from the ceiling of a train oscillates with a time period $2$ $second$ , when the train is accelerating at $10\,ms^{-2}$. What will be its time period when the train retards at $10\,ms^{-2}$ ? .... $s$
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)
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