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Question

A monkey of mass 40 kg climbs on a rope (Fig.) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey 
1. climbs up with an acceleration of $$6 \ m s^{-2}$$ 
2. climbs down with an acceleration of $$4 \ m s^{-2}$$ 
3. climbs up with a uniform speed of $$5 \ ms^{-1}$$ 
4. falls down the rope nearly freely under gravity? (Ignore the mass of the rope). 

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Solution

1. When monkey climbs up with an acceleration 'a' then 
$$T - mg = ma $$
Or T = m (g + a) 
= 40 (10 + 6) 
= 640 N 
which exceeds the maximum tension which rope can withstand (600 N), hence rope breaks. 
2. when monkey is climbing down with an acceleration a 
mg - T = ma
or T = m (g- a) 
= 40 (10 - 4) 
= 240 N 
The rope will not break. 
3. when the monkey climbs up with uniform speed then
T = mg = 40 $$\times$$ 10 
= 400 N 
The rope will not break. 
4. when the monkey is falling freely, it would be a state of weightlessness. So, there won't be any tension in the rope hence it will not break. 

Physics

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