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A thin uniform square plate ABCD of side...

A thin uniform square plate `ABCD` of side `a` and mass `m` is suspended in a vertical plane as shown in the figure. `AE` and `BF` are two massless inextensible strings. The line `AB` is horizontal. The tension in `AE` just after `BF` is cut will be

A

`(2mg)/5`

B

`mg`

C

`(2mg)/7`

D

`(3mg)/5`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `a_0` be the acceleration of centre G and `alpha` be the angular acceleration of the plate just after cutting the string BF.
`mg-T=ma_0`……..i
`tau_G=I_Galphaimplies Ta/2=(ma^2)/6alpha`
`impliesT=(maalpha)/3`…………iii

Just after cutting `BF, ` net acceleration of A is resultant of two acceleration `a_0 and alphaa//sqrt2` as shown. But the net acceleration of A in the vertical direction should be zero.
Hence, `a_0=(alphaa)/sqrt2sin45^@`
`impliesa_0=(alphaa)/2`.............ii
From eqn i , ii and iii we get
`T=(2mg)/5`
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