Properties of matterMedium
Question
A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^{8}\text{ }N/m^{2}$ and its radius is 4 mm , then maximum acceleration the lift can take is
$\_\_\_\_$ $m/s^{2}$. (take $g = 10\text{ }m/s^{2}$ and $\pi = 3.14$ )
Options
A.2.56
B.3.89
C.4.32
D.5.16
Solution
Sol. [Key Concept: Maximum stress $\sigma$ gives max tension $T = \sigma(\pi\ r^{2})$; then $T - mg = ma$ yields the acceleration.]
$${T - mg = ma }{\left( \sigma\pi r^{2} \right) - mg = ma }$$$\Rightarrow 4 \times 10^{8}\pi\left( 4 \times 10^{- 2} \right)^{2} - 16000 = 1600$ a
$$\Rightarrow a = 2.56\text{ }m/s^{2} $$
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