Question

A rope which can withstand a maximum tension of 400N hangs from a tree. If a monkey of mass 30 Kg climbs on the rope, in which of the following cases will the rope break? (take g = 10 m/s² and neglect the mass of the rope.)
(A) When the monkey climbs with constant speed of 5 m/s
(B) When the monkey climbs with constant acceleration of 2 m/s²
(C) When the monkey climbs with constant acceleration of 5 m/s²
(D) When the monkey climbs with constant speed of 12 m/s

Answer 1

Answer:

Option (C) When the monkey climbs with constant acceleration of 5 m/s²

Explanation:

Maximum Tension in the rope T = 400N

Rope will break when the acceleration of the monkey is such that the tension is maximum

Let the acceleration of the monkey is a

If the mass is m then

Then

$T-mg=ma$

Here m = 30 kg

Hence,

$400-30\times 10=30a$

$100=30a$

$\implies a=\frac{10}{3}=3.33$ m/s²

Thus if the acceleration of the monkey is greater than 3.33 m/s² then the rope will break. So when the monkey climbs with an acceleration of 5 m/s², the rope will break.

Therefore, the correct option is (C)

Answer 2

Answer:

Answer:

Option (C) When the monkey climbs with constant acceleration of 5 m/s²

Explanation:

Maximum Tension in the rope T = 400N

Rope will break when the acceleration of the monkey is such that the tension is maximum

Let the acceleration of the monkey is a

If the mass is m then

Then

T-mg=maT−mg=ma

Here m = 30 kg

Hence,

400-30\times 10=30a400−30×10=30a

100=30a100=30a

\implies a=\frac{10}{3}=3.33⟹a=

3

10

=3.33 m/s²

Thus if the acceleration of the monkey is greater than 3.33 m/s² then the rope will break. So when the monkey climbs with an acceleration of 5 m/s², the rope will break.

Therefore, the correct option is (C)