Point masses `m_(1) and m_(2)` are placed at the opposite ends of a rigid rod of length `L`, and negligible mass. The rod is to be set rotating about an axis perpendicualr to it. The position of point `P` on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity `omega_(0)` is minimum, is given by :

Options

A. `x = (m_2 L)/(m_1 + m_2)`
B. `x = (m_1 L)/(m_1 + m_2)`
C. `x = (m_1 )/(m_2)L`
D. `x = (m_2 )/(m_1)L`

Answer

A

Explanation

(a) The position of point `P` on rod through which the axis should pass so that the work required to set the rod rotating with minimum angular velocity `omega_0` is their centre of mass
so `m_1 x = m_2(L - x) rArr x = (m_2 L)/(m_1 + m_2)`.
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