Solid cylinders of radii $r_1, r_2$ and $r_3$ roll down an inclined plane from the same place simultaneously. If $r_1 > r_2 > r_3$,which one would reach the bottom first?

$A$ hollow sphere and a solid sphere having the same mass and same radius are rolled down a rough inclined plane. Which of the following statements is correct?

$A$ circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane,it takes $t \ s$. When it rolls down the plane,it takes $\left(\frac{\alpha}{2}\right)^{1/2} t \ s$,where $\alpha$ is:

Three bodies,a ring,a solid disc,and a solid sphere,roll down the same inclined plane without slipping. The radii of the bodies are identical,and they start from rest. If $V_S, V_R$,and $V_D$ are the speeds of the sphere,ring,and disc,respectively,when they reach the bottom,then the correct option is:

$A$ ring and a disc are initially at rest,side by side,at the top of an inclined plane which makes an angle $60^{\circ}$ with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is $(2-\sqrt{3}) / \sqrt{10} \ s$,then the height of the top of the inclined plane,in metres,is. . . . . . . . Take $g=10 \ m \ s^{-2}$.

$A$ solid ball of mass $m$ and radius $r$ rolls without slipping along the track shown in the figure. The radius of the circular part of the track is $R$. The ball starts rolling down the track from rest from a height of $8R$ from the ground level. When the ball reaches the point $P$,then its velocity will be