Question

Two blocks each of mass $M$ are connected to the ends of a light frame as shown in figure-$3.87$. The frame is rotated about the vertical line of symmetry. The rod breaks if the tension in it exceeds $T_{0}$. The maximum frequency with which the frame may be rotated without breaking the rod will be:

• A. $\frac{1}{2 \pi}\left[\frac{T_{0}}{M l}\right]^{1 / 2}$
• B. $\frac{1}{2 \pi}\left[\frac{M l}{T_{0}}\right]^{1 / 2}$
• C. $\frac{1}{2 \pi}\left[\frac{M T_{0}}{l}\right]^{1 / 2}$
• D. $\frac{1}{2 \pi}\left[\frac{l}{M T_{0}}\right]^{1 / 2}$

Answer 1

Answer: (A)

As $T_{0}=M \omega^{2} l $
$ \Rightarrow T_{0}=M 4 \pi^{2} f^{2} l $
$ \Rightarrow f=\frac{1}{2 \pi} \sqrt{\frac{T_{0}}{M l}} $
$\Rightarrow f=\frac{1}{2 \pi}\left[\frac{T_{0}}{M l}\right]^{1 / 2}$