A thin circular ring of mass $m$ and radius $R$ is rotating bout its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega '$ =
$\frac{{\omega \left( {m + 2M} \right)}}{m}$
$\frac{{\omega \left( {m - 2M} \right)}}{{\left( {m + 2M} \right)}}$
$\frac{{\omega m}}{{(m + M)}}$
$\frac{{\omega m}}{{\left( {m + 2M} \right)}}$
A spherical uniform body of radius $R$, mass $M$ and moment of inertia $I$ rolls down (without slipping) on an inclined plane making an angle $\theta $ with the horizontal. Then its acceleration is
Two blocks which are connected to each other by means of a massless string are placed on two inclined planes as shown in fig. After releasing from rest, the magnitude of acceleration of the centre of mass of both the blocks is $(g = 10\, m/s^2)$
We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by
If the earth were to suddenly contract to $\frac {1}{n}^{th}$ of its present radius without any change in its mass the duration of the new day will be nearly
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