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Point masses m1 and m2 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 perpendicular 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 ω0 is minimum, is given by :
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X = m1 L m2 -
X = m2 L m1 -
X = m2L m1 + m2 -
X = m1L m1 + m2
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Correct Option: C
Work required to set the rod rotating with angular velocity ω0
K.E. = (1/2)Iω²
Work is minimum when I is minimum.
I is minimum about the centre of mass
So, (m1) (x) = (m2) (L – x)
or, m1x = m2L – m2x
| ∴ x = | ||
| m1 – m2 |
