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Physics - NLM Question with Solution | TestHub

PhysicsNLMSimple Application of NLMMedium2 minPYQ_2017

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An elevator of mass $m$ is connected to a rope which pulls the elevator up with a maximum acceleration equal to $a$ . If the maximum bearable tension in the rope is $T$ , then for a safe journey the minimum diameter of the rope is [ $g$ = acceleration due to gravity]

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Answer:

Solution:

The maximum tension in the rope $= m (g + a)$
Stress in the rope $= \frac{m (g + a)}{π r^{2}}$
$∴ T = \frac{m (g + a)}{π r^{2}} = \frac{m (g + a)}{π {(\frac{d}{2})}^{2}}$
$∴ T = \frac{4 m (g + a)}{π d^{2}}$
$∴ d^{2} = \frac{4 m (g + a)}{π T}$
$∴ d = {[\frac{4 m (g + a)}{π T}]}^{\frac{1}{2}}$

Stream:MHT_CETSubject:PhysicsTopic:NLMSubtopic:Simple Application of NLM

⏱ 2mℹ️ Source: PYQ_2017

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