First slide

Elastic Modulie

Question

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 $\large \frac {40}{3\pi}\times 10^6Nm^{-2}$ . If g = 10ms^–2. Then what should be the minimum radius of the wire used if it is not to break?

Moderate

A

0.5mm
B

2mm
C

1mm
D

1.5mm

Solution

$\large T = \frac{{2{m_1}{m_2}g}}{{{m_1} + {m_2}}};\;f = T = \frac{{2 \times 1 \times 20}}{{2 + 1}} = \frac{{40}}{3}N$
$\large S = \frac{F}{A} = \frac{T}{{\pi {r^2}}} \Rightarrow \frac{{40}}{{3\pi }} \times {10^6} = \frac{{40}}{{3\pi {r^2}}}$
$\large {r^2} = {10^{ - 6}};\;r = {10^{ - 3}};\;r = 1mm$

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