1.

Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are PA, PB, PC with pA < pB < pC. 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»

(d) equal in all the vessels.

EXPLANATION:  

Let the mass of the liquids be m. The volumes of the liquids are m/ρₐ, m/ρᵦ, m/ρₑ. If the base areas of the identical vessels are a then the heights of the liquids in the vessels are m/aρₐ, m/aρᵦ, m/aρₑ. Hence the pressures at the bottom are ρₐgm/aρₐ, ρᵦgm/aρᵦ, ρₑgm/aρₑ  ie, mg/a, mg/a, mg/a So equal hence (d).



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