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A ball of density rho(0) falls from rest...

A ball of density `rho_(0)` falls from rest from a point P onto the surface of a liquid of density `rho` in the time T. It enters the liquid, stops, moves up, and returns to P in a total time 3 T. neglect viscosity, surface tension and splashing find the ratio of `(rho)/(rho_(0))`

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AI Generated Solution

To solve the problem, we need to find the ratio of the densities \(\frac{\rho}{\rho_0}\) given the conditions of the ball falling into the liquid and the time taken for its motion. We will break down the solution step by step. ### Step 1: Understand the motion of the ball The ball falls from a height and takes time \(T\) to reach the surface of the liquid. After entering the liquid, it stops, moves back up, and returns to the original point \(P\) in a total time of \(3T\). ### Step 2: Determine time spent in the liquid Since the total time for the entire motion is \(3T\) and the time taken to fall to the surface is \(T\), the time spent inside the liquid can be calculated as: \[ ...
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