A sphere pure rolls on a rough inclined plane with initial velocity 2.8 m/s. Find the maximum distance on the inclined plane.

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc

Assertion The angular momentum of system always remain constant.

Reason For a system, $$\tau_{\mathrm{ext}}=\frac{d L}{d t}=0$$

A boy is pushing a ring of mass $$3 \mathrm{~kg}$$ and radius $$0.6 \mathrm{~m}$$ with a stick as shown in figure. The stick applies a force of $$3 \mathrm{~N}$$ on the ring and rolls it without slipping with an acceleration of 0.4 m/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 $$\frac{F}{10}$$. The value of $$F$$ is

Assertion : The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies.

Reason : For all solid bodies, total kinetic energy is always twice of translational kinetic energy.