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Work Energy Theorem

A wire of 10×...

Question

A wire of $10 \times 10^{- 3} k g$ mass per meter passes over a frictionless pulley fixed on the top of an inclined frictionless plane which makes an angle of $30^{o}$ with the horizontal. Masses $M_{1}$ and $M_{2}$ are tied at the two ends of the wire. The $M_{1}$ rests on the plane and the mass $M_{2}$ hangs freely vertically downwards. The whole system is in equilibrium. Now a tranverse wave propagates along the wire with a velocity of 100 m/s. The ratio of mass $M_{1}$ and $M_{2}$ is

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Solution

Step 1: Draw a free body diagram of the given problem.

Step 2: Calculate the tension in the wire.

Formula Used:
Wave velocity: $v = \sqrt{\frac{T}{μ}}$

$100 = \sqrt{\frac{T}{10 \times 10^{- 3}}}$ $\Rightarrow$ T = 100 N

Step 3: Find the ratio of masses $M_{1}$ and $M_{2}$
The blocks are in equilibrium

$T = M_{1} g s i n 30^{0} \Rightarrow 100 = M_{1} \times 10 \times \frac{1}{2}$

$\Rightarrow M_{1} = 20 k g$

$T = M_{2} g \Rightarrow 100 = M_{2} 10 \Rightarrow M_{2} = 10 k g$

So,

$\frac{M_{1}}{M_{2}} = \frac{20}{10} = 2$

Final answer:(2)

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Standard XII Physics

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