First slide

Stress and strain

Question

Two bodies of masses 1 kg and 2 kg are connected by a metal wire as shown in fig.
A force of10 Nis applied on the body of mass 2 kg. The breaking stress of metal wire is 2 x 10⁹ N/m². What should be the minimum radius of the wire used, if it is not to break ?

Moderate

A

0.23x 10^-4 m
B

4x10^-4m
C

5x 10^-4 m
D

5.2x 1O^-4 m

Solution

The free body force diagram is shown in fig.

From figure ,F-T=2a and T =1x a=a
$∴$ F-a = 2a or F = 3a or a = F/3
Therefore, a =(10 / 3)m/s²
Now T=a(10 / 3)
$Stress = \frac{T}{{πr}^{2}} or 2 \times 10^{9} = \frac{(10 / 3)}{3 \cdot 14 \times r^{2}}$
$\begin{array}{l} ∴ r^{2} = \frac{(10 / 3)}{3 \cdot 14 \times (2 \times 10^{9})} = \frac{10}{3 \times 3 \cdot 14 \times (2 \times 10^{9})} \\ r = \sqrt{[\frac{10}{3 \times 3 \cdot 14 \times (2 \times 10^{9})}]} \end{array}$
or $r = 0 \cdot 23 \times 10^{- 4} m$

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