A 4⋅0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of $19 \cdot 2 \times 10^{- 3} kg m^{- 1}$ . Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2⋅0 m s⁻². Take g = 10 m s⁻².

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Solution

Given,
Mass of the block = 4.0 kg
Linear mass density, $m = 19.2 \times 10^{- 3} kg / m$
From the free body diagram,
$T - 4 g - 4 a = 0 \Rightarrow T = 4 (a + g) = 4 (2 + 10) = 48 N$

$Wave speed, ν = \sqrt{(\frac{T}{m})} = \sqrt{\frac{48}{19.2 \times 10^{3}}} = \sqrt{(2.5 \times 10^{- 3})} = 50 m / s$

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Given, Mass of the block = 4.0 kg Linear mass density, m=19.2×10-3 kg/m From the free body diagram, T-4g-4a=0⇒T=4a+g =42+10=48 N Wave speed, ν=Tm =4819.2×103 =2.5×10-3=50 m/s