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  4. A taut string having tension 50 N and linear mass density 0.25 kg m- 1 is used inside a cart to generate a wave pulse starting at the left end. The velocity of cart so that the pulse remains stationary with respect to the ground is -α hatims- 1 . Write the value of 100α . (. Take, √2=1.414)

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Q. A taut string having tension $50\, N$ and linear mass density $0.25\, kg\, m^{- 1}$ is used inside a cart to generate a wave pulse starting at the left end. The velocity of cart so that the pulse remains stationary with respect to the ground is $-\alpha \hat{i}ms^{- 1}$ . Write the value of $100\alpha .$
$\left(\right.$ Take, $\sqrt{2}=1.414)$

NTA AbhyasNTA Abhyas 2022

Solution:

$v=\sqrt{\frac{T}{\mu }}$
$=\sqrt{\frac{50}{0 . 25}}=\sqrt{200}=10\sqrt{2}=14.14\, m/s$
$\therefore \overset{ \rightarrow }{V}_{P}=\overset{ \rightarrow }{V}_{P C}+\overset{ \rightarrow }{V}_{C G}$
$0=14.14\hat{i}+\overset{ \rightarrow }{v}_{C G}$
$\overset{ \rightarrow }{v}_{CG}=-14.14\hat{i}\, m/s$