One end of a thin uniform rod of length L and mass M₁ is rivetted to the centre of a uniform circular disc of radius 'r' and mass M₂ so that both are coplanar. The centre of mass of the combination from the centre of the disc is (Assume that the point of attachment is at the origin).

Easy

A

$\large \frac{{{\rm{L(}}{{\rm{M}}_{\rm{1}}} + {M_2})}}{{{\rm{2}}{{\rm{M}}_{\rm{1}}}}}$
B

$\large \frac{{{\rm{L}}{{\rm{M}}_{\rm{1}}}}}{{{\rm{2(}}{{\rm{M}}_{\rm{1}}} + {{\rm{M}}_{\rm{2}}})}}$
C

$\large \frac{{{\rm{2(}}{{\rm{M}}_{\rm{1}}} + {{\rm{M}}_{\rm{2}}})}}{{{\rm{L}}{{\rm{M}}_{\rm{1}}}}}$
D

$\large \frac{{{\rm{2L}}{{\rm{M}}_{\rm{1}}}}}{{({{\rm{M}}_{\rm{1}}} + {{\rm{M}}_{\rm{2}}})}}$

Solution

Distance from M₂ is
$\large x_2=\frac {M_1d}{M_1+M_2}=\frac {M_1(L/2)}{M_1+M_2}=\frac {M_1L}{2(M_1+M_2)}$

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