Question

A stone of mass of $16kg$ is attached to a string $144$ m long and is whirled in a horizontal smooth surface. The maximum tension the string can withstand is $16$ N. The maximum speed of revolution of the stone without breaking it, will be

• A. $20m{s}^{-1}$
• B. $16m{s}^{-1}$
• C. $14m{s}^{-1}$
• D. $12m{s}^{-1}$

Answer 1

Answer: (D)

$12m{s}^{-1}$

Centripetal force is given by:
$F=\frac{m{v}^2}{R}$
Which is equal to the tension.
For max velocity.
$T_{max}=\frac{m{v}_{max}^2}{R}$
$v_{max}=\sqrt{\frac{TR}{m}}=\sqrt{\frac{16\times 144}{16}}=12m{s}^{-1}$
Hence option D is correct.