Question

A bob of mass $10\, kg$ is attached to wire $0.3$ long. Its breaking stress is $4.8 \times 10^{7} Nm ^{2}$. The area of cross section of the wire is $10^{-6} m ^{2} .$ The maximum angular velocity with which it can be rotated in a horizontal circle

• A. 8 rad/ sec
• B. 4 rad/ sec
• C. 2 rad/ sec
• D. 1 rad/ sec

Answer 1

Answer: (B)

Using the relation
Force =breaking stress $\times$ area
$=\left(4.8 \times 10^{7}\right)\left(10^{-6}\right)=48\, N$ ...(1)
Using the relation
$F=M r \omega^{2}$ ...(2)
$M r \omega^{2} =48$
$10 \times 0.3 \times \omega^{2}=48$
$\omega^{2}=\frac{48}{10 \times 0 \cdot 3}=16$
so $\omega^{2}=16$
$\omega= 4\, rad / \sec$