A uniform annular disc of radii $R_0$ and $2R_0$ and mass $M$ rolls without slipping on a rough horizontal surface under the action of a constant horizontal force $F_0$ (see figure). Then [Moment of inertia of annular disc about its own axis is $\frac{5}{2}M{R}_0^2$]

For the uniform square lamina of mass $2.0 \mathrm{kg}$, side length $40\mathrm{cm}$ and centre at $C,I_{IJ}$ represents moment of inertia about the axis passing through points $I$ and $J$, and $I_K$ represents moment of inertia about the axis passing through point $K$ and perpendicular to the plane of the lamina. Then

Statement-I: If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.

Statement-2: The linear momentum of an isolated system remains constant.

Statement-I: Two cylinders, one hollow (metal) and the other solid (wood), with the same mass and identical dimensions, are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.

and

Statement-2: By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

In the arrangement shown the fixed pulley is massless and frictionless. If the acceleration of block of mass $1 \mathrm{kg}$ is $\frac{30}{x} \mathrm{m} {\mathrm{s}}^{-2}$. Find the value of $x$.

In the given arrangement the block is released from the position where the spring is unstretched. The speed of the block when it has descended through $2\mathrm{cm}$ is $\frac{x}{10}$. Find the value of $x$.