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A heavy block of mass 150 kg hangs with ...

A heavy block of mass `150 kg` hangs with the help of three vertical wires of equal length and equal cross-sectional area as shown in Fig.
Wire is attached to the mid-point (centre of mass) of block. Take `Y_(2) = 2Y_(1)`. For this arrangement mark out the correct statement(s).

A

The wire I and III should have same Young's modulus.

B

Tension in I and III would be always equal.

C

Tension in I and III would be different.

D

Tension in II is `75g`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Here for all three wires length `l`, elongaton `/_\l` and cross sectioinal area `A` are the same. From
`Y="Stress"/"Strain"=(T//A)/(/_\l//l)`
`rarr TpropY`
Let `T_(1), T_(2)` and `T_(3)` be tension in thre wires I, II and III, respectively.
For vertical eqilibrium
`T_(1)xxT_(2)+T_(3)=150g`
For rotation equilibrium
`T_(1)xx x-T_(3)x=0`
`impliesT_(1)=T_(3)` so `Y_(1)=Y_(3)`
`implies(T_(2))/(T_(1))=(T_(2))/(Y_(1))=2`
`implies T_(2)=2T_(1)`
so `2T_(1)+T_(2)=150g`
`impliesT_(2)=75g`
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