The linear acceleration of a car is 10m/s². If the wheels of the car have a diameter of 1m, the angular acceleration of the wheels will be

The correct option is 20 rad/sec².

To find the angular acceleration of the wheels of the car, we can use the relationship between linear acceleration and angular acceleration for rolling motion without slipping.

First, let us note the given information from the problem:

Linear acceleration of the car, $a=10{\text{m/s}}^2$

Diameter of the wheels, $d=1\text{m}$

The radius $r$ of the wheels is calculated as half of the diameter:

$r=\frac{d}{2}=\frac{1\text{m}}{2}=0.5\text{m}$

The relation between the linear acceleration ($a$) of the vehicle and the angular acceleration ($\alpha$) of its wheels is:

$a=r\alpha$

Rearranging the equation to solve for angular acceleration ($\alpha$):

$\alpha =\frac{a}{r}$

Substituting the values into the equation:

$\alpha =\frac{10{\text{m/s}}^2}{0.5\text{m}}=20{\text{rad/s}}^2$

Thus, the angular acceleration of the wheels is 20 rad/sec².