A solid spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \mathrm{~m} / \mathrm{s}$ at the bottom of the inclination. How far will the ball go up the plane?

(Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A metre stick is balanced on the knife edge at its centre. When four coins, each of mass 2 g are put one on top of the other at 10.0 cm mark, the stick it found to be balanced at 46.0 cm mark. The mass of the metre stick is

A wheel of radius with 0.5 m and a moment of inertia of $10 \mathrm{~kg}-\mathrm{m}^2$ is rotating freely at an angular speed of 70 $\mathrm{rev} / \mathrm{min}$. The wheel can be stopped in 5.0 s by pressing a wet cloth against the rim and exerting a radially inward force of 88 N . The coefficient of kinetic friction between the wheel and wet cloth is

A solid cylinder of mass $m$ and radius $R$ rolls down on an inclined plane of height 30 m without slipping. The speed of its centre of mass, when the cylinder reaches the bottom is

[use $g=10 \mathrm{~m} / \mathrm{s}^2$ ]