A disc and a solid sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?

Options

A. Disk
B. Sphere
C. Both reach at the same time
D. Depends on their masses

Answer

B

Explanation

`a= (g sin theta)/(1+ (K^(2))/(R^(2)))` for disc, `(K^(2))/(R^(2))= (1)/(2) = 0.5`
for sphere, `(K^(2))/(R^(2))= (2)/(5)= 0.4`
a (sphere) `gt` a (disc)
`therefore` sphere reaches first.
Aliter:
`t= (1)/(sin theta) sqrt((2h)/(g) (1+ (K^(2))/(R^(2))))`
`rArr t_("sphere") lt t_("disc")`