A monkey of mass 40 kg climbs on a rope which can withstand a maximum tension of 600 N In which of the following cases will the rope break : The monkey
(a) climbs up with an acceleration of `6 ms^(-2)`
(b) climbs down with an acceleration of `4 ms^(-2)`
(c) climbs up with a uniform speed of `5 ms^(-1)`
(d) falls down the rope nearly freely under gravity ? (Ignore the mass of the rope.)

Explanation

(a) When the monkey climbs up with an acceleration a, then T - mg = ma where T represents the tension ( figure a )
`therefore` T = mg + ma = m(g + a)
or T = 40 kg (10 +6) `ms^(-2)` = 640 N
But the rope can without a maximum tension of 600 N . So the rope will break.
(b) When the monkey is climbing down with an acceleration, then
mg - T = ma (Figure (b) )
`implies` T = mg - ma = m(g -a)
or T = 40 `kg xx (10 - 4) ms^(-2)` = 240 N
The rope will not break.
(c ) When the monkey climba up with uniform speed , then T mg = `40 kg xx 10 ^(ms^-2)` = 400 N . The rope will hot break.
(d) When the monkey is falling freely, it would be a state of weightlessness. tension will be zero and the rope will not break.