PhysicsTwo blocks of masses 1 kg and 2kg are connected by a metal wire going over a smooth pulley as shown. The breaking stress of the metal is 403π x 106 Nm-2. If g = 10ms–2. Then what should be the minimum radius of the wire used if it is not to break?

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

A
0.5mm
B
2mm
C
1mm
D
1.5mm

Solution:

$T = \frac{2 m_{1} m_{2}}{m_{1} + m_{2}}; f = T = \frac{2 x 1 x 20}{2 + 1} = \frac{40}{3}$

$S = \frac{F}{A} = \frac{T}{{πr}^{2}} \Rightarrow \frac{40}{3 π} x 10^{6} = \frac{40}{3 {πr}^{2}}$
$\Rightarrow$ r² = 10^-6 $\Rightarrow$ r = 10^–3 $\Rightarrow$ r = 1mm

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