91Ó°ÊÓ

• Mass of bolt,$\mathrm{m}=30.0\text{g}$ .
• Radius,$\mathrm{r}=3.5\text{cm}$
• Strobe rate,$2000\text{flashespersecond}.$

The problem deals with the centripetal force. It is a force that makes a body follow a curved path.From the given information, the time period can be calculated. The force on the bolt from the rod is the centripetal force which can be calculated using its formula.

Formula:

Centripetal force is given by,

$\mathrm{F}=\frac{{\mathrm{mv}}^2}{\mathrm{r}}$

We note that the period$\mathrm{T}$is eight times the time between flashes$\left(\frac{1}{2000}\text{ s}\right)$.

So $\mathrm{T}=0.0040\text{s}$.

We know that,

$\mathrm{T}=\frac{2\mathrm{Ï€°ù}}{\mathrm{v}}$

Also, centripetal force is given by,

$\mathrm{F}=\frac{{\mathrm{mv}}^2}{\mathrm{r}}$

Combining the above two equations leads to,

$\mathrm{F}=\frac{4{\mathrm{³¾Ï€}}^2\mathrm{R}}{{\mathrm{T}}^2}$

Substitute the values in the above equation, and we get,

$\begin{array}{l}\mathrm{F}=\frac{4\left(0.030\text{ k²µ}\right){\mathrm{Ï€}}^2\left(0.035\text{″¾}\right)}{{\left(0.0040\text{ s}\right)}^2}\\ \mathrm{F}=2.6×{10}^3\text{ N}\end{array}$

Thus, the magnitude of the force is $2.6×{10}^3\text{ N}$.