A disc initially at rest, is rotated about its axis with a uniform angular acceleration. In the first $2$ $s$ , it rotates an angle $\theta$. In the next $2\, s$, the disc will rotate through an angle

If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass then duration of the new day will be

The centre of mass of a body

A thin circular ring of mass $M$ and radius $R$ is rotating about 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 rotates now with an angular velocity

Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices  $A, B, C$ and $D$ of a square of side $1\, m$. The coordinates of centre of  mass of the particles are

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