A massless string is wrapped round a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the fig. If the mass is released then its velocity while touching the ground level will be
$\sqrt {2gh} $
$\sqrt {2gh} \,\frac{M}{m}$
$\sqrt {2ghm/M} \,$
$\sqrt {4mgh/2m + M} \,$
Three thin rods each of length $L$ and mass $M$ are placed along $x, y$ and $z-$ axes is such a way that one end of each of the rods is at the origin. The moment of inertia of this system about $z-$ axis is
Four particles of masses $m_1 = 2m,\, m_2 = 4m,\, m_3 = m$ and $m_4$ are placed at four corners of a square. What should be the value of $m_4$ so that the centres of mass of all the four particles are exactly at the centre of the square?
The linear mass density of a rod of length $L$ varies as $\lambda = kx^2$, where $k$ is a constant and $x$ is the distance from one end. The position of centre of mass of the rod is
The mass per unit length of a rod of length $l$ is given by : $\lambda = \frac{M_0x}{l}$ ,where $M_0$ is a constant and $x$ is the distance from one end of the rod. The position of centre of mass of the rod is
A wheel of mass $10\,kg$ has a moment of inertia of $160\,kg-m^2$ about its own axis. The radius of gyration is ........ $m.$