A reel of massless thread unrolls itself falling down under gravity. The acceleration of its fall is :

Options

A. g
B. `(g )/(2)`
C. `(2)/(3)g`
D. `(4)/(5)g`.

Answer

D

Explanation

Here
`mgh=(1)/(2)mv^(2) +(1)/(2)Iomega^(2)`
`=(1)/(2)mv^(2)+(1)/(2)xx(mr^(2))/(2)xx omega^(2)`
`=(1)/(2)mv^(2)+(1)/(4)mv^(2)=(3)/(4)mv^(2)`
`v^(2)=(4)/(3)gh" Now " v^(2)-u^(2)=2as`
`(4)/(3) gh-0=2ah or a=(2)/(3)g`.
Correct choice is (d).