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A monkey of mass 40kg climbs on a rope w...

A monkey of mass `40kg` climbs on a rope which can stand a maximum tension of `600N`. In which of the following cases will the rope break ? The monkey
`(a)` climbs up with acceleration of `6ms^(-2)` .
`(b)` climbs down with acceleration of `4ms^(-2)`
`(c )` climbs up with uniform speed of `5ms^(-1)`
`(d)` falls down the rope nearly freely under gravity `(g=10ms^(-2))`.

Text Solution

Verified by Experts

`(a)` `(b)`
`(c )` `(d)`
`m=40kg`, `g=10ms^(-2)`
`(a) a=6ms^(-2)` `T-mg=ma`
`T=mg+ma=m(g+a)=40(10+6)=640N gt 600N`
Hence the rope will break when the monkey climbs up with an acceleration `6ms^(-2)`.
`(b) mg-T=ma^(1)`
`:.T=m(g-a)=40(10-40)=240N`
`(c )` Hence `T=mg`
`T=40xx10=410N`
`(d)` `mg-T=mg`
`:.T=0`
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