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$A$ copper wire is held at the two ends by rigid supports. At $50^{\circ} C$ the wire is just taut,with negligible tension. If $Y=1.2 \times 10^{11} \, N/m^2$,$\alpha=1.6 \times 10^{-5} /^{\circ} C$,and $\rho=9.2 \times 10^3 \, kg/m^3$,then the speed of transverse waves in this wire at $30^{\circ} C$ is .......... $m/s$.

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$A$ wire of linear mass density $\mu = 10^{-2} \, kg \, m^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^o$ with the horizontal. Masses $m$ and $M$ are tied at two ends of the wire such that $m$ rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 \, m \, s^{-1}$.

The linear density of a vibrating string is $1.3 \times 10^{-4} \, kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $Y = 0.021 \, \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is ..... $N$.

Two $Cu$ wires of radii $R_{1}$ and $R_{2}$ are such that $(R_{1} > R_{2})$. Then which of the following is true?

$A$ $43\, m$ long rope of mass $5.0\, kg$ joins two rock climbers. One climber strikes the rope and the second one feels the effect $1.4\, s$ later. What is the tension in the rope in $N$?

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