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A vessel contains two immiscible liquids...

A vessel contains two immiscible liquids of density `rho_(1)=1000 kg//m^(3)` and `rho_(2)=1500kg//m^(3)`. A solid block of volume `V=10^(3)m^(3)` and density `d=800kg//m^(3)` is tied to one end of a string and the outer end is tied to the bottom of the vessel as shown in figure.
The block is immersed with two fifths of its volume in the liquid of lower density. The entire system is kept in an elevator which is moving upwards with an acceleration of `a=g/2`. Find the tension in the string.

A

1. 8N

B

2. 6N

C

3. 10N

D

4. 12N

Text Solution

Verified by Experts

The correct Answer is:
B
We analysed this problem from the reference frame of elevator.
Total buoyant force on the block,
`F_(B)=((2)/(5)Vrho_(2)+(3)/(5)Vrho_(1))(g=a)`
For equilibrium,
`F_(B)=T+Vd(g+a)`
or `T=F_(B)-Vd(g+a)`
`=(g+a)V[(2)/(5)rho_(2)+(3)/(2)rho_(1)-d]`
`T=(10+(10)/(2))xx10^(-3)[(2)/(5)xx1500+(3)/(5)xx1000-800]=6 N`
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