Question

When a force $F_1$ acts on a particle, frequency $6$Hz and when a force $F_2$ acts, frequency is 8 Hz. What is the frequency when both the force act simultaneously in same direction?

• A. $12$Hz
• B. $25$Hz
• C. $10$Hz
• D. $5$Hz

Answer 1

Answer: (C)

$10$Hz

$F=mr{\omega }^2=mr\times (2\pi mm{)}^2=4{\pi }^{2}m{m}^2$
$F\propto 2n^2$
$F=F_1+F_2$
$n^2=n_1^2+n_2^2$
$n=\sqrt{n_1^2+n_2^2}$
$n=\sqrt{(6{)}^2+(8{)}^2}$
$n=\sqrt{100}=10$Hz.