The maximum tension a rope can withstand is $60 k g w t$ . The ratio of maximum acceleration with which two boys of masses $20 k g$ and $30 k g$ can climb up the rope at the same time is:

1 : 2

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2 : 1

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4 : 3

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3 : 2

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Solution

The correct option is D $3 : 2$
Given: Maximum tension $= 60 k g w t$
$M_{1} = 20 k g$ and $M_{2} = 30 k g$

$\Rightarrow 60 g = 20 (g + a_{1}) + 30 (g + a_{2})$
$\Rightarrow 60 g = 20 g + 20 a_{1} + 30 g + 30 a_{2}$
$\Rightarrow 20 a_{1} + 30 a_{2} = 10 g$
$\Rightarrow 2 a_{1} + 3 a_{2} = g$
So, the pair of values which can satisfy the above equation is:
$a_{1} = \frac{g}{4}$ and $a_{2} = \frac{g}{6}$
$\Rightarrow a_{1} : a_{2} = 3 : 2$

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Similar questions

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A monkey of mass 20kg climbs on a rope which can stand a maximum tension of 300 N.in which of the following cases the rope breaks? The monkey

Options

Climbs up with an acceleration of 6m/s2

Climbs up with a uniform speed of 5m/s

Climbs down with an acceleration of 4m/s2

Falls down the rope nearly freely under gravity

Ans :1st option

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