If a disc slides from top to bottom of an inclined plane, it takes time `t_(1)`. If it rolls, it takes time `t_(2)`. Now, `(t_(2)^(2))/(t_(1)^(2))` is

Options

A. `(1)/(2)`
B. `(2)/(3)`
C. `(3)/(2)`
D. `(2)/(5)`

Answer

C

Explanation

Here the time `t_(1)=sqrt((2l)/(gsintheta))`
Also the rolling time `t_(2)=sqrt((3l)/(gsintheta))`
`therefore (t_(2)^(2))/(t_(1)^(2))=(3)/(2)`