A metal cylinder is suspended vertically in equilibrium by a cord. The diagram shows the cylinder in four different positions P, Q, R and S.

Question 20

A metal cylinder is suspended vertically in equilibrium by a cord. The diagram shows the cylinder in four different positions P, Q, R and S.

Which statement explains the variation of the tension T in the cord?

A At P and at Q, the tension T in the cord is the same because the difference in pressure

between the top and bottom of the cylinder is the same.

B At Q, the tension T in the cord is less than at P because, at smaller depth, liquid pressure is smaller.

C At R, the tension T in the cord is less than at P because atmospheric pressure is less than water pressure.

D At S, the tension T in the cord is greater than at P because atmospheric pressure at S exerts no force on the top or bottom of the cylinder.

Reference: Past Exam Paper – June 2017 Paper 12 Q10

Solution:

Answer: A.

At position S, the weight of the metal cylinder acts downwards. Since it is in equilibrium, the tension T is equal to the weight W.

As the cylinder is lowered in the water, an upthrust force U acts on it.

The tension T = W – U

The upthrust force is due to the difference in pressure exerted by the water on the top and bottom surfaces. However, at R, the cylinder is not fully submerged. So, the upthrust at R is not the same as at P or Q.

Pressure in liquid, P = hρg

ΔP = Δhρg

The change in pressure is proportional to the change in depth under water. Δh is the height of the cylinder.

So, whatever the position under the water, as long as the cylinder is fully submerged, the difference in pressure, and thus, the upthrust force is the same.

 

It is correct that the liquid pressure is less at smaller depth, but the difference in pressure between the bottom and top of the cylinder is the same at position P and position Q, so the tension in the cord at P and Q will be the same.