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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