Questions
Point masses and 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 is minimum, is given by
detailed solution
Correct option is B
Moment of inertia of the system about the axis of rotation (through point P ) isI=m1x2+m2(L-x)2 By work energy theorem, Work done to set the rod rotating with angular velocity ω0= Increase in rotational kinetic energy W=12Iω02=12m1x2+m2(L-x)2ω02 For W to be minimum, dWdx=0 i.e. 122m1x+2m2(L-x)(-1)ω02=0 or m1x-m2(L-x)=0 ∵ω0≠0 or m1+m2x=m2L or x=m2Lm1+m2Similar Questions
Three point masses, each of m, are placed at the corners of an equilateral triangle of side l. Then the moment of inertia of this system about an axis along one side of the triangle is
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