Question

A disc of mass 5 kg and radius 50 cm rolls on the ground at 10 m/s. Find the kinetic energy.

Hint:

For a rolling disc: Total KE = \( \frac{3}{4}mv^2 \) — memorize this shortcut!

Answer 1

Correct Answer: 375

Concept: Total kinetic energy of a rolling body: \[ K = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 \] For a disc: \[ I = \frac{1}{2} mR^2, \quad v = \omega R \]

Step 1: \[ K = \frac{1}{2}mv^2 + \frac{1}{2} \cdot \frac{1}{2} mR^2 \cdot \frac{v^2}{R^2} \] \[ = \frac{1}{2}mv^2 + \frac{1}{4}mv^2 \]

Step 2: \[ K = \frac{3}{4}mv^2 \]

Step 3: \[ K = \frac{3}{4} \times 5 \times (10)^2 = \frac{3}{4} \times 5 \times 100 = 375 \, J \]