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Partially Inelastic Collision

A wire of mas...

Question

A wire of mass $9.8 \times 10^{- 3} k g / m$ passes over a friction-less pulley fixed on the top of an inclined plane which makes an angle of $30^{o}$ with horizontal. Two masses $M_{1}$ , $M_{2}$ are attached to the two ends of the wire. $M_{1}$ is at rest on an inclined plane and $M_{2}$ is hanging vertically downwards. The system is in equilibrium. If a transverse wave progresses with a velocity of $100 m / s$ in the wire then the values of $M_{1}$ , $M_{2}$ are :

A

20 k g, 40 k g

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B

10 k g, 30 k g

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C

20 k g, 10 k g

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D

10 k g, 40 k g

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Solution

The correct option is C $20 k g, 10 k g$
Velocity $v = \sqrt{\frac{T}{μ}}$
$\Rightarrow T = v^{2} μ$
$10^{4} \times 9.8 \times 10^{- 3}$ $= 98 N$
$T = M_{1} g sin 30$
$\Rightarrow M_{1} = \frac{98}{9.8 \times \frac{1}{2}} = 20 k g$
$M_{2} g = T$
$\Rightarrow M_{2} = 10 k g$

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