A sphere, disc and a ring each having same mass M and radius R roll down without slipping from an inclined plane. Which of three will reach foot of inclined plane first :

Options

A. Ring
B. Disc
C. Sphere
D. All the three will reach at same time.

Answer

C

Explanation

We know that acceleration down the inclined plane is
`a=(gsintheta)/(1+1//MR^(2))`
For sphere `I=(2)/(5)MR^(2)`
`therefore a_("shere")=(5)/(7)gsintheta=0.7gsintheta`
For disc `I=(1)/(2)MR^(2)`
`therefore a_("disc")=(2)/(3)gsintheta=0.66gsintheta`
For ring `I=MR^(2)`
`therefore a_("ring")=(1)/(2)gsintheta=0.5gsintheta`
Since acceleration is maximum for sphere therefore sphere will reach the ground first.