Four solid spheres each of diameter $\sqrt{5} \mathrm{cm}$ and mass $0.5 \mathrm{kg}$ are placed with their centres at the corners of a square of side $4 \mathrm{cm}$. The moment of inertia of the system about the diagonal of the square is $\mathrm{N}\times {10}^{-4} \mathrm{kg} {\mathrm{m}}^2$, then $\mathrm{N}$ is

A boy is pushing a ring of mass $2 \mathrm{kg}$ and radius $0.5 \mathrm{m}$ with a stick as shown in Fig. 11.153. The stick applied a force of $2\mathrm{N}$ on the ring and rolls it without slipping with an acceleration of $0.3 \mathrm{m}/{\mathrm{s}}^2$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is $(P/10)$. Find the value of $P$.

A uniform circular disc of mass $1.5 \mathrm{kg}$ and radius $0.5 \mathrm{m}$ is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude $F=0.5 \mathrm{N}$ are applied simultaneously along the three sides of an equilateral triangle $XYZ$ with its vertices on the perimeter of the disc (see Fig. $11.154$). Find the angular speed of the disc in radian per sec, one second after applying the forces.