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(D) The tension $T$ in the wire when the lift is accelerating upwards is given by $T = m(g + a)$.Given $m = 9 \, kg$, $g = 10 \, ms^{-2}$, and $a = 2

Vedclass · Accepted Answer

$7.5 \, g \, cm^{-3}$

Vedclass · Answer

(D) The tension $T$ in the wire when the lift is accelerating upwards is given by $T = m(g + a)$.Given $m = 9 \, kg$, $g = 10 \, ms^{-2}$, and $a = 2 \, ms^{-2}$, we have $T = 9(10 + 2) = 9 	imes 12 = 108 \, N$.The speed of a transverse wave on a wire is given by $v = \sqrt{\frac{T}{\mu}}$, where $\mu$ is the linear mass density.We know $\mu = ho A$, where $ho$ is the density of the material and $A$ is the cross-sectional area.Given $v = 120 \, ms^{-1}$ and $A = 1 \, mm^2 = 10^{-6} \, m^2$, we have $v^2 = \frac{T}{ho A}$.Rearranging for $ho$, we get $ho = \frac{T}{v^2 A} = \frac{108}{(120)^2 	imes 10^{-6}} = \frac{108}{14400 	imes 10^{-6}} = \frac{108}{0.0144} = 7500 \, kg \, m^{-3}$.Converting to $g \, cm^{-3}$, $ho = 7500 	imes 10^{-3} \, g \, cm^{-3} = 7.5 \, g \, cm^{-3}$.Thus, the correct option is $D$.

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