A dumbbell has spherical ends of masses M and 2M, each volume V, connected by a light rod. In water of density ρ, adding a mass m at the shown point makes both spheres exactly half submerged and the rod horizontal. Find the geometric ratio asked in the figure. Image
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Question

A dumbbell has spherical ends of masses M and 2M, each volume V, connected by a light rod. In water of density ρ, adding a mass m at the shown point makes both spheres exactly half submerged and the rod horizontal. Find the geometric ratio asked in the figure. Image

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G1 Physics · Accepted Answer

Step 1: Use hydrostatic equilibrium, P₂−P₁ = ρgΔh; in an accelerating fluid replace g by the effective acceleration where required. Step 2: Equate pressures at the same horizontal level or integrate pressure over the stated surface. Applying these relations to the given data gives B: d(Vρ−2M)/[2(Vρ−3M)]. Final answer: B.