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A unifrom disc is acted by two equal for...

A unifrom disc is acted by two equal forces of magnitude `F`. One of them, acts tangentially to the disc, while other one is acting at the central point of the disc. The friction between disc surface and ground surface in `nF`. If `r` be the radius of the disc, then the value of `n` would be (in `N`)

A

`0`

B

`1.2`

C

`2.0`

D

`3.2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f` be the frictional force between disc surface and ground surface. Let `a` be the linear acceleration of the disc. For the motion of the disc, we can write
`2F - f = ma` …(i)
and `(F + f) r = I alpha`
where `I = (1)/(2)mr^(2) and alpha = (a)/(r )`
`:. (F + f)r = (1)/(2)mr^(2) xx (a)/(r ) = (1)/(2)mra` ..(ii)
Putting value of `ma` from (i) in (ii), we get
`(F + f) r = (1)/(2) (2F - f)r`
or `F + f = F - f//2 or f = 0 = nF` (Given)
So `n = 0`
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