A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500 N. In which of the following cases will the rope break? `("Take g"=10m s^(-2))`

Options

A. The monkey climbs up with an acceleration of `5ms^(-2)`.
B. The monkey climbs down with an acceleration of `5ms^(-2)`.
C. The monkey climbs up with a uniform speed `5ms^(-2)`.
D. The monkey falls down, the rope freely under gravity.

Answer

A

Explanation

Here, mass of monkey, m=40kg
Maximum tension, the rope can stand, T=500N
Tension in the rope will be equal to apparent weight of the monkey (R ).
The rope will break R exceeds T.
(a) When the monkey climbs up with an acceleration `a=5ms^(-2)`
`R=m(g+a)=40(10+5)=600N therefore R gt T`
Hence, the rope will break.
(b). When the monkey climbs down with an acceleration `a=5ms^(-2)`
`R=m(g-a)=40(10-5)=200N therefore R lt T`
Hence, the rope will not break.
(c ). When the monkey falls down the rope freely under gravity `a=g therefore R=m(g-a)=m(g-g)=zero`
Hence, the rope will no break