question_answer

Two masses \[M\] and \[m\] are attached to a vertical axis by weightless threads of combined length \[l\]. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity \[\omega \]. If the tensions in the threads are the same during motion, the distance of \[M\] from the axis is                               [MP PET 1995]

A)             \[\frac{Ml}{M+m}\]

B)                      \[\frac{ml}{M+m}\]

C)             \[\frac{M+m}{M}l\]

D)                      \[\frac{M+m}{m}l\]

Correct Answer: B

Solution :

                If the both mass are revolving about the axis yy' and tension in both the threads are equal then             \[M{{\omega }^{2}}x=m{{\omega }^{2}}(l-x)\]             Þ \[Mx=m(l-x)\]             Þ \[x=\frac{ml}{M+m}\]