A monkey of mass 40 kg climbs on a rope as shown in figure which can stand 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

Mass of monkey m= 40 kg
maximum tension that rope can withstand
`T_(max) = 600 N`
(a) When monkey moves upward with acceleration a

`T- mg - ma`
`T= m(g + a)`
`=40 (10+ 6)`
`=640 N`
Hence `T gt T _(max)` hence rope will break
(b ) When monkey moves in downward directin with acceleration of `4ms^(2)`

`T= mg -a`
`=40(10-4)`
`240 N`
`T lt T _(max)`
rope will not break
(c ) When monkey moves in upward direction with constant velocity of ` 5ms^(-1)` pseude acceleration is zero
`:. T = mg`
`=40 xx 10`
` =400 N`
Hene `T lt T_(max)` rope will not break .
( d ) When monkey is falling freely due to gravitation its pseudo acceleration will be g
T = m( g- a) a=g
`=40 (g - g)`
`T= 0 N`
Here monkey is in weigthlessness conditiion hence tension in the is zero and rope will not break .