MHTCET 15 May 2024 Shift 2 Paper

Concept:The speed of a transverse wave in a string depends on the tension and the mass per unit length of the string.Explanation:The wave velocity in a string is given by $v = \sqrt{\frac{T}{\mu}}$, so the tension is $T = \mu v^2$.First, convert the mass per unit length to SI units:$\mu = 10^{-6} \text{ kg/cm} = 10^{-4} \text{ kg/m}$.The given wave equation is $Y = 0.2 \sin(2x + 80t)$ m.Comparing it with the standard equation $y = A \sin(kx + \omega t)$, we get:Wave number $k = 2$ and angular frequency $\omega = 80$.The wave velocity is $v = \frac{\omega}{k} = \frac{80}{2} = 40 \text{ m/s}$.Substitute $v$ and $\mu$ into the tension formula:$T = (40)^2 \times 10^{-4}$$T = 1600 \times 10^{-4} = 0.16 \text{ N}$.Answer:The tension in the string is $0.16 \text{ N}$.Hence, option A is correct.