Chapter 39, Problem 42P

(a)

To determine

Verification of the statement that the expression $\left(\frac{\Delta t_{\text{R}}-\Delta t_0}{\Delta t_0}\right)$ is equal to $\left(-\frac{r^2{\omega }^2}{2c^2}\right)$ when $r\omega$ is very less than $c$ .

(b)

To determine

Verification of the statement that the clock experiences a pseudo force $F_r$ of $mr{\omega }^2$ in rotating frame and that this is tantamount to gravitational potential difference $\left({\varphi }_r-{\varphi }_0\right)$ of $\left(-\frac{r^2{\omega }^2}{2}\right)$ .

(c)

To determine

Verification of the statement that the difference in time intervals in rotating frame is same as in inertial frame.