A particle executes $S.H.M.$ according to equation $x=10( cm ) \cos \left[2 \pi t+\frac{\pi}{2}\right]$, where $t$ is in second. The magnitude of the velocity of the particle at $t=\frac{1}{6} \,s$ will be .............. $cm / s$
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The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$.The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is true
A $15 \,g$ ball is shot from a spring gun whose spring has a force constant of $600 \,N/m$. The spring is compressed by $5 \,cm$. The greatest possible horizontal range of the ball for this compression is .... $m$ ($g = 10 \,m/s^2$)
The periodic time of a body executing simple harmonic motion is $3\, sec$. After how much interval from time $t = 0$, its displacement will be half of its amplitude ..... $\sec$
Four harmonic waves of equal frequencies and equal intensities $I_0$ have phase angles $0, \pi / 3,2 \pi / 3$ and $\pi$. When they are superposed, the intensity of the resulting wave is $nI _0$. The value of $n$ is
Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m$. the rod is pivoted at its centre $‘O’$ and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is