Question

A monkey of mass 20kg climbs on a rope which can stand a maximum tension of 300 N.in which of the following cases the rope breaks? The monkey

Options

Climbs up with an acceleration of 6m/s2

Climbs up with a uniform speed of 5m/s

Climbs down with an acceleration of 4m/s2

Falls down the rope nearly freely under gravity

Ans :1st option

Answer 1

You have changed the values of question.
But provided the answer as per the original question. then how can we do.

Let me try with the original question,
Here mass of monkey is 40kg and
maximum tension is 600 N

(a) F = T – mg(bcz climbing up)
ma = T – mg
T = ma + mg
= m(a + g)
= 40(10 +6)
=640N
This is greater than the max. tension which the rope can withstand. Hence the rope will break.

(b)F = mg – T (bcz climbing down)
ma = mg – T
T = mg - ma
=m(g - a)
= 40(10 - 4)
= 240N
This is lesser than the max. tension which the rope can withstand. Hence the rope will not break.

( c) F = T – mg (bcz climbing up)
ma = T – mg
T = ma + mg
= m(a + g)
= 40(0+ 10)
=400N
This is greater than the max. tension which the rope can withstand. Hence the rope will not break.

( d) F = mg – T
ma = mg – T
T = mg - ma
=m(g - g)
= 0 N
so rope wont break .