Answer
The fraction of the total kinetic energy that is due to the rotation of the wheels is $~~\frac{1}{51}$
It is not necessary to know the radius of the wheels because the rotational kinetic energy of the wheels depends on the mass of the wheels and the car's speed.
Work Step by Step
Let $M_c$ be the mass of the car.
Let $M_w$ be the mass of each wheel.
Let $v$ be the speed of the car.
Note that $M_c = 100~M_w$
We can find an expression for the total kinetic energy:
$K = \frac{1}{2}M_c~v^2+\frac{1}{2}I\omega^2$
$K = \frac{1}{2}M_c~v^2+\frac{1}{2}(4\times \frac{1}{2}M_w~R^2)(\frac{v}{R})^2$
$K = \frac{1}{2}M_c~v^2+M_w~v^2$
$K = \frac{1}{2}(100~M_w)~v^2+M_w~v^2$
$K = 51~M_w~v^2$
Note that the rotational kinetic energy is $M_w~v^2$
We can find the fraction of the total kinetic energy that is due to the rotation of the wheels:
$\frac{K_{rot}}{K} = \frac{M_w~v^2}{51~M_w~v^2} = \frac{1}{51}$
The fraction of the total kinetic energy that is due to the rotation of the wheels is $~~\frac{1}{51}$
It is not necessary to know the radius of the wheels because the rotational kinetic energy of the wheels depends on the mass of the wheels and the car's speed.
