Two blocks of masses 1kg and 2kg are connected by a metal wire going over a smooth pulley. The breaking stress of metal is $\frac{40}{3 π} \times 10^{6} {Nm}^{- 2}$ . What should be the minimum radius of wire used if it should not break? (g = 10ms^-2)

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1.5mm

1mm

2mm

0.5mm

answer is B.

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Detailed Solution

$T = [\frac{2 m_{1} m_{2}}{m_{1} + m_{2}}] g$
$F = T = \frac{40}{3} N; S = \frac{F}{A} = \frac{T}{{πr}^{2}}$
$\frac{40}{3 π} \times 10^{6} = \frac{40}{3 {πr}^{2}}$
$r^{2} = 10^{- 6} \Rightarrow r = 10^{- 3} m$
$\Rightarrow r = 1 mm$

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