A rod of length 6 m has specific gravity 25/36. One end is tied to a 5 m rope fastened at the floor of a 10 m deep pool. Find the length of rod above water (m) in the shown equilibrium.
Physics · Mixed Chapter
JEE Main Practice

Question

A rod of length 6 m has specific gravity 25/36. One end is tied to a 5 m rope fastened at the floor of a 10 m deep pool. Find the length of rod above water (m) in the shown equilibrium.

G1 Physics · Accepted Answer

Step 1: Let immersed length be s and emerged length 6−s. Buoyancy is ρ_water g A s; rod weight is (25/36)ρ_water g A×6. Step 2: The tether adds a force and torque. Therefore, unlike free flotation, s is not determined by equating just buoyancy with weight. Step 3: Use the geometry of the 5-m tether and 10-m depth together with the moment balance about its attachment point. Step 4: The PDF's answer is 1 m above water. A fully determined algebraic solution requires the rope angle/rod orientation…