Question

5) Consider a uniform thin rod with length L. I_1 is the moment of inertia of this rod about an axis perpendicular to the rod a quarter length from its center. I_2 is the moment of inertia of the rod with respect to an axis perpendicular to it through its center. which relationship between the two inertia's is correct?

a) I_1 = I_2. b) I_1 > I_2. c) I_1 < I_2. d) they could be the same or different depending on the mass and length of the rod.

6) If the amplitude of the simple harmonic motion of a mass-spring system is doubled, the mechanical energy of the system:

a) decreases by a factor of sqrt(2). b) increases by a factor of sqrt(2). c) decreases by a factor of 4. d) increases by a factor of 4. e) decreases by a factor of 2. f) increases by a factor of 2. g) does not change

Answer 1

Question 5

As per the parallel axis theorem, the moment of inertia about an axis at a distance from the centre is equal to the the moment of inertia about the axis passing through the centre plus the mass times the square of the distance between them.

Clearly,

Hence, Option B is correct.

Question 6

The initial mechanical energy is

, where is the amplitude.

Doubling the amplitude, we get

It increases by a factor of four, hence Option D is correct.