Question

The moment of inertia of two bodies 4 kg 9 kg respectively have same rotational kinetic energy the calculate the ratio of angular momentum

a. 1:3
b. 1:9
c. 9:1
d. 3:1

Answer 1

To calculate the ratio of the angular momenta, we can use the principle of conservation of kinetic energy. The correct ratio is 9:1. Option C is correct.

Step-by-step explanation:

To compare the ratio of the angular momenta, we can use the principle of conservation of kinetic energy. The rotational kinetic energy of a body is given by the formula:

Rotational kinetic energy = ½ * moment of inertia * angular speed^2

Since the two bodies have the same rotational kinetic energy, we can set up the following equation:

½ * I1 * π1^2 = ½ * I2 * π2^2

Dividing both sides of the equation by ½ and canceling like terms, we get:

I1 * π1^2 = I2 * π2^2

Now we can calculate the ratio of the angular momenta:

Angular momentum ratio = (I1 * π1) / (I2 * π2)

Plugging in the given values:

Angular momentum ratio = (4 * π1) / (9 * π2)

Simplifying further:

Angular momentum ratio = 4 / 9

Therefore, the ratio of angular momenta is 4:9. The correct answer is option (c) 9:1.