A flywheel rotates at constant speed of 3000 rpm. The angle described by the shaft in radian in one second is

The correct option is 100 π.

To find the angle described by the shaft in radians in one second, we need to convert the rotational speed of the flywheel from revolutions per minute (rpm) to radians per second.

First, let's identify the given values:
Rotational speed, $N=3000\text{rpm}$ (revolutions per minute)

We know that in one complete revolution, a shaft rotates through an angle of:
$\theta =2\pi \text{radians}$

Since the flywheel completes 3000 revolutions in one minute, the total angle rotated in one minute (60 seconds) is:
$\text{Total angle in 60 seconds}=3000\times 2\pi \text{radians}$

To find the angle described in one second, we divide the total angle rotated in 60 seconds by 60:
$\text{Angle in one second}=\frac{3000\times 2\pi }{60}\text{radians}$

Simplifying the expression:
$\text{Angle in one second}=50\times 2\pi =100\pi \text{radians}$

Thus, the angle described by the shaft in one second is 100 π radians.