Question

A block of mass $M$ is situated on a smooth horizontal friction less table. A thread tied to a 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. $\frac{2Ml{\omega }^2}{g}$

Answer 1

The correct option is A $\frac{Ml{\omega }^2}{g}$

$\begin{array}{c}T=M{w}^{2}l\\ T=mg\\ \Rightarrow mg=M{w}^{2}l\\ \Rightarrow m=\frac{M{w}^{2}l}{g}\end{array}$

Hence,

option $\left(A\right)$ is correct answer.