Question

Two cylinders of same cross-section and length L but made of two material of densities d₁ are cemented together to form a cylinder of length 2L. The combination floats in a liquid of density d with a length L/2 above the surface of the liquid. If d₁ < d₂ then –

• A. (a) d₁ < $\frac{3}{4}$ d
• A. (b) $\frac{d}{2}$ > d₁
• A. (c) $\frac{d}{4}$ > d₁
• A. (d) d < d₁

Answer 1

(a)

Net weight = upthrust

(d₁ + d₂) LAg = $\frac{3}{2}$ LAdg

(d₁ + d₂) = $\frac{3}{2}$ d

As d₁ < d₂

\ d₁ < $\frac{3}{4}$ d