An inclined plane makes an angle $30^{\circ}$ with the horizontal. $A$ solid sphere rolls down from the top of the inclined plane from rest without slipping. Its linear acceleration along the plane is equal to (where $g$ is acceleration due to gravity and $\sin 30^{\circ} = 0.5$):

$A$ solid sphere rolls purely on an inclined plane of inclination $\theta$. Which of the following statements are correct?
$(1)$ The friction force acting on the sphere is $f = \mu mg \cos \theta$.
$(2)$ Friction is a dissipative force.
$(3)$ Friction increases angular velocity and decreases linear velocity.
$(4)$ If $\theta$ decreases,friction decreases.

Consider a situation in which a ring,a solid cylinder,and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and have identical diameters. The correct statement for this situation is:

What is the velocity of a sphere starting from rest and rolling without slipping down an inclined plane of vertical height $h$?

$A$ solid sphere rolls down without slipping from the top of an inclined plane of height $28 \text{ m}$ and angle of inclination $30^{\circ}$. The velocity of the sphere, when it reaches the bottom of the plane is (Acceleration due to gravity $= 10 \text{ ms}^{-2}$)

$A$ body starts rolling down an inclined plane of length $L$ and height $h$. This body reaches the bottom of the plane in time $t$. The relation between $L$ and $t$ is: