$A$ solid sphere rolls down an inclined plane and its velocity at the bottom is $v_1$. Then the same sphere slides down the plane (without friction) and let its velocity at the bottom be $v_2$. Which of the following relations is correct?

Which of the following is true about the angular momentum of a cylinder rolling down a slope without slipping?

$A$ cylinder of mass $10 \; kg$ and radius $15 \; cm$ is rolling perfectly on a plane of inclination $30^{\circ}$. The coefficient of static friction $\mu_{S} = 0.25$.
$(a)$ How much is the force of friction acting on the cylinder?
$(b)$ What is the work done against friction during rolling?
$(c)$ If the inclination $\theta$ of the plane is increased,at what value of $\theta$ does the cylinder begin to skid and not roll perfectly?

$A$ solid sphere rolls on a surface with a translational velocity $v \ m/s$. It climbs up a curved surface without slipping. The minimum value of $v$ required to reach the height $h$ is:

$A$ cylinder is pure rolling up an incline plane. It stops momentarily and then rolls back. The force of friction

$A$ solid spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \ m/s$ at the bottom of the inclination. How far will the ball go up the plane (in $cm$)? (Use $g=10 \ m/s^2$)