Question

During the phenomenon of resonance, the amplitude of oscillation becomes large. The variation of g with angular velocity \( \omega \) is given by \[ g' = g - R\omega^2 \] If Earth were to spin faster, that is, angular velocity increases, then except at poles, the weight of bodies will decrease at all places.

• A. 1
• B. 0.5
• C. 0.25
• D. 2

Hint:

The modulation index in AM waves is calculated by dividing the message signal's amplitude by the carrier wave's amplitude.

Answer 1

The Correct Option is B

In this case, the modulation index \( \mu \) is determined from the maximum amplitude of the message signal \( A_m \) and the amplitude of the carrier wave \( A_c \). The modulation index is defined as: \[ \mu = \frac{A_m}{A_c} \] Given: - \( A_m = 20 \, \text{cm} \), - \( A_c = 40 \, \text{cm} \), We can substitute these values into the equation to get: \[ \mu = \frac{20}{40} = 0.5 \] Thus, the modulation index is \( 0.5 \), so the correct answer is (B).