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The metallic bob of simple pendulum has the relative density $5$. The time period of this pendulum is $10\,s$. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt{ x } s$. The value of $x$ will be.
The potential energy of a particle of mass $1\, kg$ in motion along the $x-$ axis is given by $U = 4\,(1 -cos\,2x)$, where $x$ is in $metres$ . The period of small oscillation (in $second$ ) is
A man measures the period of a simple pendulum inside a stationary lift and finds it to be $T$ sec. If the lift accelerates upwards with an acceleration $\frac{g}{4}$, then the period of the pendulum will be
A loaded vertical spring executes $S.H.M.$ with a time period of $4\; sec$. The difference between the kinetic energy and potential energy of this system varies with a period of ........$sec$
Two particles P and Q describe S.H.M. of same amplitude $a$, same frequency $f$ along the same straight line. The maximum distance between the two particles is a $\sqrt{2}$.The initial phase difference between the particle is -
A wooden cube (density of wood $'d'$ ) of side $'l'$ floats in a liquid of density $'\rho '$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period $'T'$. Then, $'T'$ is equal to