If a cycle wheel of radius 4 m completes one revolution in two seconds. Then acceleration of the cycle will be

The correct option is 4π² m / s².

To find the acceleration of the cycle wheel, we can analyze the motion of a point on the rim of the wheel. Since the wheel is executing uniform circular motion, any point on its rim experiences a centripetal acceleration directed towards the center of the wheel.

The formula for centripetal acceleration is given by:
$a={\omega }^{2}r$
where:
- $a$ is the centripetal acceleration,
- $\omega$ is the angular velocity,
- $r$ is the radius of the wheel.

First, we calculate the angular velocity ($\omega$). The angular velocity is defined as:
$\omega =\frac{2\pi }{T}$
where $T$ is the time period of one revolution.

According to the problem statement:
- Radius, $r=4\text{m}$
- Time period, $T=2\text{s}$

Substituting $T=2\text{s}$ into the angular velocity formula:
$\omega =\frac{2\pi }{2}=\pi \text{rad/s}$

Now, substituting the values of $\omega$ and $r$ into the acceleration formula:
$a={\pi }^2\times 4$
$a=4{\pi }^2{\text{m/s}}^2$

Thus, the acceleration of the cycle wheel is $4{\pi }^2{\text{m/s}}^2$.