Q191 / 200 · Manipal (MET) 2013 · Physics

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

  • A
    12 Hz
  • B
    25 Hz
  • Correct answer
    C
    10 Hz
  • D
    5 Hz

Solution

$\begin{aligned} & F=m r \omega^2=m r \times(2 \pi m r n)^2=4 \pi^2 m r^2 \\ & F \propto 2 n^2\end{aligned}$ $\begin{aligned} F & =F_1+F_2 \\ n^2 & =n_1^2+n_2^2 \\ n & =\sqrt{n_1^2+n_2^2} \\ n & =\sqrt{(6)^2+(8)^2} \\ n=\sqrt{100} & =10 \mathrm{~Hz}\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions