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A disc – like reel with massless thread ...

A disc – like reel with massless thread unwinds itself while falling vertically downwards. The acceleration of its fall is:

A

Zero

B

g

C

`(2g)/(3)`

D

`(g)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let us consider the instant the reel has descended distance h Loss of PE = Translational KE + Rotational KE
`:. Mgh = (1)/(2) mv^(2) + (1)/(2) I omega^(2)`
`mgh = (1)/(2) mv^(2) + (1)/(2) ((1)/(2) mr^(2)) (v^(2))/(r^(2))`
`gh = (3)/(4) v^(2)` , `v^(2) = (4)/(3) gh`
`v^(2) = 2ah, (4)/(3) gh = 2ah, a = (2g)/(3)`
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