Question

Two masses $M$ and $m$ are attached to a vertical axis by weightless threads of combined length $\ell$. 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 :

• A. $\frac{M\ell }{M+m}$
• B. $\frac{m\ell }{M+m}$
• C. $\frac{M+m}{M}\ell$
• D. $\frac{M+m}{m}\ell$

Answer 1

The correct option is B $\frac{m\ell }{M+m}$

Let tension in the string be $T$ and distance of mass $M$ from the axis be $x$.

For mass M : $T=Mx{w}^2$ .........(1)

For mass $m$ : $T=m(l-x)w^2$ ............(2)

Equating (1) & (2) we get

$Mx{w}^2=m(l-x)w^2$

$⟹$ $x=\frac{ml}{m+M}$