First slide

Elastic Modulie

Question

Two block of masses of 1 kg and 2 kg 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? (Take, g = 10 ms^-2). [Manipal 2012]

Moderate

A

0.5 mm
B

1 mm
C

1.5 mm
D

2 mm

Solution

Breaking stress $= \frac{F}{A} = \frac{40}{3 π} \times 10^{6} {Nm}^{- 2}$
According to question,
$\frac{40}{3 π} \times 10^{6} = \frac{3 \times 10}{π r^{2}}$
$\Rightarrow r^{2} = \frac{9}{4 \times 10^{6}}$
$\Rightarrow r = 1.5 \times 10^{- 3} m$
= 1.5 mm

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