A monkey of mass 40 kg climbs on a rope which can withstand a maximum tesion 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 unifrom speed of `5 ms^(-1)` (d) falls down the rope nearly freely under gravity Ignore the mass of the rope .

Explanation

Here , mass of monkey , ` m = 40 kg`
Maximum tension the rope can withstand , `T = 600 N`
In each case actual tension in the rope will be equal to apparent weight of monkey
The rope will break when R exceeds T (a) When monkey climbs up with `a = 6 ms^(-2)`
`R = m (g + a ) = 40 (10 + 6) = 640` N (which is greater than T)
Hence the rope will break .
(b) When monkey climbs down with `a = 4 ms^(-2),R = m (g - a) = 40 (10 - 4) = 240 N`
Which is less than T `:.` The rope will not break
(c) When monkey climbs up with a unifrom speed `upsilon = 5 ms^(-1)` , its acceleration
`a = 0 :. R = m ( g - a ) = m (g -g )` = Zero
Hence the rope will not break
.