Question

A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500N. In which of the following cases will the rope break? (Take $g = 10m{s^{ - 2}}$)
A.)The monkey climbs up with an acceleration of $5m{s^{ - 2}}$
B.)The monkey climbs down with an acceleration of $5m{s^{ - 1}}$
C.)The monkey climbs up with a uniform speed of $5m{s^{ - 1}}$
D.)The monkey falls down the rope freely under gravity

Answer 1

Hint: These types of questions usually can be solved using the formula of Tension i.e. $T = mg + ma$ also takes acceleration - $5m{s^{ - 1}}$ when the monkey is climbing down the tree.

Complete step-by-step answer:
For option, A acceleration of money climbing the rope is a =$5m{s^{ - 2}}$ upward

According to the question mass of the monkey = 40 kg maximum tension that rope can bear is 500N i.e. T max = 500 N and $g = 10m{s^{ - 2}}$.

Tension in a body is expressed as $T = mg + ma$ (equation 1)

Here g is the gravitational force and a is the acceleration.

Substituting the given values in equation 1

$T = m(g + a)$
$\Rightarrow$ $T = 40(10 + 5)$
$\Rightarrow$ $T = 600N$

Since T > T max

Hence the rope will break in this case

When the monkey climbs down with an acceleration of $5m{s^{ - 1}}$
Since the monkey is going down the acceleration will be -$5m{s^{ - 1}}$

Substituting the values in equation 1

$T = m(g + a)$
$\Rightarrow$ $T = 40(10 - 5)$
$\Rightarrow$ $T = 200N$
Since T < T max

Therefore the rope will not break in this case

When the monkey climbs up with a constant speed of $5m{s^{ - 1}}$

Therefore the acceleration of the monkey is 0 i.e. a = 0

Substituting the values in equation 1

$T = m(g + a)$
$\Rightarrow$ $T = 40(10 + 0)$
$\Rightarrow$ $T = 400N$
Since T < T max

Therefore the rope will not break in this case

When the monkey falls down the rope freely under gravity
Therefore the acceleration of the monkey is a = g

Substituting the values in equation 1

$T = m(g + a)$
$\Rightarrow$ $T = 40(g - g)$
$\Rightarrow$ $T = 0N$
Since T < T max

Therefore the rope will not break in this case.

Since the rope breaks when the monkey is climbing at the acceleration of $5m{s^{ - 2}}$
Hence, option A is the correct answer.

Note: The only term that has played an important role in the above solution is tension, which can be explained as the force that is transmitted through a rope, string, or wire when pulled by forces acting from opposite sides. At the ends, the tension force is directed over the wire’s length and pulls energy equally on the bodies.