# Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of a) 0.42 m from the mass of 0.3 kg b) 0.70 m from the mass of 0.7 kg c) 0.98 m from the mass of 0.3 kg d) 0.98 m from the mass of 0.7 kg

## Question ID - 100736 :- Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of a) 0.42 m from the mass of 0.3 kg b) 0.70 m from the mass of 0.7 kg c) 0.98 m from the mass of 0.3 kg d) 0.98 m from the mass of 0.7 kg

3537

(c)

The moment o inertia of the system about axis of rotation  is

+

The work done in rotating the rod is converted into its rotational kinetic energy

For work done to be minimum

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 Let  be the moment of inertia of a uniform plate about an axis  that passes through its centre and is parallel to two of its sides.  is a line in the plane of the plate that passes through the centre of the plate and makes an angle  with . The moment of inertia of the plate about the axis  is then equal to a) b) c) d)