Question

A string of mass $3$kg is under tension of $400$N. The length of the stretched string is $25$cm. If the transverse jerk is stuck at one end of the string find the velocity?

• A. $25{\pi }^{2}m{s}^{-2}$
• B. $-5{\pi }^{2}m{s}^{-2}$
• C. $5{\pi }^{2}m{s}^{-2}$
• D. $-25{\pi }^{2}m{s}^{-2}$

Answer 1

The correct option is B $-5{\pi }^{2}m{s}^{-2}$

Here, A = $5cm=0.05$m, T = $0.2$s

$\therefore \omega =\frac{2\pi }{T}=\frac{2\pi }{0.2}=10\pi rad{s}^{-1}$

Velocity and acceleration of the particle executing SHM at any displacement xi given by

Velocity, $v=\omega \sqrt{A^2-x^2}$
and acceleration, $a=-{\omega }^{2}x$
when $x=5cm=0.05$m
$\therefore v=10\pi \sqrt{(0.05{)}^2-(0.05{)}^2}=0anda=-\left(10\pi {)}^2\right(0.05)=-5{\pi }^{2}m{s}^{-2}$