Question

A string of length $1$ m is fixed at one end and carries a mass of $100$ g at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end. If angle of inclination of the string with the vertical is ${\cos }^{-1}5/8$, the linear velocity of the mass is nearly:

• A. 1 $m{s}^{-1}$
• B. 2 $m{s}^{-1}$
• C. 3 $m{s}^{-1}$
• D. 4 $m{s}^{-1}$

Answer 1

Answer: (C)

3 $m{s}^{-1}$

Using $u=r\omega =r\times 2\pi f$
$=1\sin \theta \times 2\pi f$, we get $(\therefore r=1\sin \theta )$
$u=1\times 0.78\times 2\pi \times \frac{2}{\pi }$
$=3.12m{s}^{-1}$