question_answer

A wire of \[9.8\times {{10}^{-3}}kg{{m}^{-1}}\] passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of 30° with the horizontal. Masses m and M are tied at the two ends of 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 ms?1. Chose the correct option

A)            \[m=20\,kg\]

B)            \[m=5\,kg\]

C)            \[m=2\,kg\]

D)            \[m=7\,kg\]                          

Correct Answer: A

Solution :

 \[v=\sqrt{\frac{T}{\mu }}\] For equilibrium \[Mg=mg\sin 30=T\] Þ \[M=\frac{m}{2}\] Þ \[100=\sqrt{\frac{Mg}{9.8\times {{10}^{-3}}}}=\sqrt{\frac{M(9.8)}{9.8\times {{10}^{-3}}}}\] Þ \[100=\sqrt{M(1000)}\] Þ \[M=10kg\] and \[m=20kg\]