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  4. Two blocks of masses 40 kg and 20 kg are connected by a wire that has a linear mass density of 1 g / m. These blocks are being pulled across horizontal frictionless floor by horizontal force F that is applied to 20 kg block. A transverse wave travels on the wave between the blocks with a speed of 400 m / s (relative to the wire). The mass of the wire is negligible compared to the mass of the blocks. The magnitude of F is

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Q. Two blocks of masses $40 \,kg$ and $20 \, kg$ are connected by a wire that has a linear mass density of $1 \, g / m$. These blocks are being pulled across horizontal frictionless floor by horizontal force $F$ that is applied to $20 \, kg$ block. A transverse wave travels on the wave between the blocks with a speed of $400 \, m / s$ (relative to the wire). The mass of the wire is negligible compared to the mass of the blocks. The magnitude of $F$ is

Waves

Solution:

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Tension $T$ in the wire $=v^{2} \rho$
$=(400)^{2} \times 10^{-3}=160 \,N$
Force applied $F=\frac{T\left(m_{1}+m_{2}\right)}{m_{1}}$
$=160 \times \frac{(40+20)}{40}=240 \,N$