Question

A 4 kg block is suspended from the ceiling of an elevator through a spring having a linear mass density of $19.2\times {10}^{-3}kg{m}^{-3}$. Find the speed with respect to spring with which a wave pulse can proceed on the spring if the elevator accelerates up at the rate of 2.0 ms${}^{-2}$ Take g = 10 ms${}^{-2}$

• A. 30 m/s
• B. 42 m/s
• C. 46 m/s
• D. 50 m/s

Answer 1

The correct option is D 50 m/s

Since the lift is accelerating up the effective gravity is $g_{eff}=12m/s^2$ and the tension in the string is $T=m{g}_{eff}=4\times 12=48N$
Speed of the wave is $=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{48}{19.2\times {10}^{-3}}}=50m/s$