Question

What is the moment of inertia of a rod about an axis passing through the centre and perpendicular to its central axis? Given that mass of rod is 1kg, length = 10cm.

• A. 0.0063kgm^2
• B. 0.083kgm^2
• C. 0.00083kgm^2
• D. 0.083kgm^2

Answer 1

Answer: (C)

0.00083kgm^2

Answer 2

The moment of inertia of a rod about an axis passing through its center and perpendicular to its length is given by the formula:

$I = \frac{1}{12}ML^2$

Given:

• Mass of the rod (M) = 1 kg
• Length of the rod (L) = 10 cm = 0.1 m

Substitute the given values into the formula:

$I = \frac{1}{12} \times 1 \text{ kg} \times (0.1 \text{ m})^2$ $I = \frac{1}{12} \times 1 \times 0.01$ $I = \frac{0.01}{12}$ $I \approx 0.0008333 \text{ kgm}^2$

Rounding to two significant figures, we get:

$I \approx 0.00083 \text{ kgm}^2$

The calculated value matches the third option.