Question

Equal mass of three liquids are kept are kept in three identical cylindrical vessels A, B and C. The densities are ρₐ, ρᵦ, ρₑ with ρₐ<ρᵦ< ρₑ. The force on the base will be

(a) maximum in vessel A

(b) maximum in vessel B

(c) maximum in vessel C

(d) equal in all the vessels

Answer 1

Answer ⇒ Option (d). Equal in all vessel.

Explanation ⇒ Since, the three cylinder is identical. Thus, there base area, there height all is same.

Now, For A,

Pa = P₀ + hρg

Pa = P₀ + h × m/(A × h) × g

Pa = P₀ + mg/A

Now, From this we can see that Pa does not depends upon density of fluids. It only depends upon mass of fluid. which is same for all three vessel.

Therefore, Pa = Pb = Pc =  P₀ + mg/A

Hence, Option (d). is correct.

Hope it helps.