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A striaght rod of length L has one of its end at the origin and its length varies with position as x directly proportional to L .if the mass per unit length of rod is given by Ax where Ais constant ,where is the centre of mass? [AIIMS2015]

A striaght rod of length L has one of its end at the origin and its length varies with position as x directly proportional to L .if the mass per unit length of rod is given by Ax where Ais constant ,where is the centre of mass?
                                                                         [AIIMS2015]
 
 
 
 

Grade:12

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Distance of center of mass from the origin=\dfrac{\int_0^L (\lambda dx)x}{\int_0^L\lambda dx}

=\dfrac{\int_0^L(Ax)xdx}{\int_0^L(Ax)dx}

=\dfrac{\int_0^Lx^2dx}{\int_0^Lxdx} =\dfrac{2L}{3}

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