Question

Two blocks each of mass M are connected to the ends of a light frame as shown in below figure. The frame is rotated about the vertical line of symmetry. The rod breaks if the tension in it exceeds $T_0$. Find the maximum frequency with which the frame may be rotated without breaking the rod.

• A. $\frac{1}{2\pi }{\left[\frac{T_0}{Ml}\right]}^{\frac{1}{2}}$
• B. $\frac{2\pi }{l}M{T}_0$
• C. $2\pi {\left[\frac{T_0}{Ml}\right]}^{\frac{1}{2}}$
• D. $\frac{1}{2\pi l}M{T}_0$

Answer 1

The correct option is A

$\frac{1}{2\pi }{\left[\frac{T_0}{Ml}\right]}^{\frac{1}{2}}$

Consider one of the blocks. If the frequency of revolution is f, the angular velocity is $\omega$ = 2 $\pi$f.The

acceleraton towards the centre is $\frac{v^2}{l}$ = ${\omega }^{2}l$ = $4{\pi }^2{f}^{2}l$. The only horizontal force on the block is the

tension of the rod. At the point of breaking, this force is $T_0$.So from Newton's second law,

$T_0=M.4{\pi }^2{f}^{2}l$

or f = $\frac{1}{2\pi }{\left[\frac{T_0}{Ml}\right]}^{\frac{1}{2}}$