Question

Derive expression for velocity of a ring, solid cylinder and solid sphere having same radii rolling down the smooth inclined plane without slipping.

Answer 1

$v = \sqrt{2gh \div (1 + ( {k}^{2} \div {r}^{2} ))}$

${k}^{2} \div {r}^{2} for \: ring = 1 \\ for \: solid \: cylinder = \frac{1}{2} \\ for \: solid \: sphere = \frac{2}{5}$

derivation-

applying come

k1+u1=k2+u2

0+mgh=1/2mv^2(1+ksq/r sq)

on rearranging u get it