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
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The equation of motion of a particle is $\frac{{{d^2}y}}{{d{t^2}}} + Ky = 0$, where $K$ is positive constant. The time period of the motion is given by
Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $K$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The amplitude of oscillations is
Two simple harmonic motions of angular frequency $100$ and $1000\,\,rad\,s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is
A load of mass $m$ falls from a height $h$ on to the scale pan hung from the spring as shown in the figure. If the spring constant is $k$ and mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is
A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will
$Assertion :$ For a particle performing $SHM$, its speed decreases as it goes away from the mean position.
$Reason :$ In $SHM$, the acceleration is always opposite to the velocity of the particle.
If a Second's pendulum is moved to a planet where acceleration due to gravity is $4$ times, the length of the second's pendulum on the planet should be made .......... times
A cylindrical plastic bottle of negligible mass of filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega $. If the radius of the bottle is $2.5\, cm$ then $\omega $ is close to ..... $rad\, s^{-1}$ (density of water $= 10^3\, kg/m^3$)
The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be