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  • Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking strees of the metal is <img alt="\frac{24}{\pi }\times 10^{2}\, Nm^{-2}," src="https://entrancecorner.codecogs.com/gif.latex?%5Cfrac%7B24%7D%7B%5Cpi%

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking strees of the metal is \frac{24}{\pi }\times 10^{2}\, Nm^{-2}, What is the minimum radius of the wire ?
(take g = 10 ms-2 )

Option: 1 1250 cm
Option: 2 1.25 cm
Option: 3 125 cm
Option: 4 12.5 cm

Answers (1)

best_answer

Tension\, in\, the\, wire= T= \frac{2m_{1}m_{2}g}{\left ( m_{1}+m_{2} \right )}
                                                    = \frac{2\times 3\times 5\times 10}{8}
                                               T= 37\cdot 5\, N= \frac{75N}{2}
Breaking \, Stress= \frac{T}{A}= \frac{\frac{75}{2}}{\pi r^{2}}= \frac{24}{\pi }\times 10^{2}
                                           r^{2}= \frac{75}{2\times 24}\times 10^{-2}
                                                = \frac{75}{48}\times 10^{-2}
                                           r^{2}= \frac{25}{16}\times 10^{-2}
                                           r= \frac{5}{4}\times 10^{-1}
                                               = 1\cdot 25\times 10^{-1}m
                                               = 12\cdot 5\times 10^{-2}m
                                      \Rightarrow r= 12\cdot 5\, cm
The correct option is (4) 

Posted by

vishal kumar

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