Question

A block of mass $M$ is situated on a smooth horizontal frictionless table. A thread tied to the block passes through a hole in the table and carries a mass m at its other end. If the length of the thread above the table is $l$, what should be the value of m so that it may remain suspended at a constant height and the block $M$ moves in a circular path with an angular velocity $\omega$ on the table ?

• A. $\frac{Ml \omega^{2}}{g}$
• B. $\frac{Ml \omega^{2}}{3g}$
• C. $\frac{Ml \omega^{2}}{5g}$
• D. $\frac{2 Ml \,\omega^{2}}{g}$

Answer 1

Answer: (A)

The situation is shown in figure. For the mass $m$ to be stationary, the tension in the string should provide the necessary centripetal force on the rotating mass $M$. Now
$T=mg$ and $T=Ml \omega^{2}$
or $mg =ml \omega^{2}$
or $m=\frac{Ml \omega^{2}}{g}$