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Two monkeys of masses 10 kg and 8 kg, are moving along a vertical rope which is light and inextensible, the former climbing up with acceleration $2m/{{s}^{2}}$ while the later coming down with velocity of 2m/s. Find the tension (In Newtons)
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A. 200 N
B. 150 N
C. 300 N
D. 100 N

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Last updated date: 13th Jun 2024
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Answer
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Hint: In this question two monkeys are moving in the opposite directions, so, the net tension will be the addition of the forces exerted by the individual monkey on the rope. Now, one of the monkeys is moving at a constant velocity, so only gravitational force will act on it. While, the other has some acceleration, another force will be acting on it in addition to the gravitational force

Complete step-by-step answer:
Before we start solving the question that is given to us, let us take a look at all the parameters that are given in the question
Let the mass of the monkey which is climbing up the rope be ${{m}_{1}}$
So, we have
${{m}_{1}}=10kg$
Also, the velocity of the monkey that is climbing up is given to us,
a = $2m/{{s}^{2}}$
So, the forces acting on the rope due to the monkey going up will be
\[{{F}_{up}}={{m}_{1}}a+{{m}_{1}}g\]
Using the give values
We have
\[\Rightarrow {{F}_{up}}=10\times 2+10\times 10\]
For the ease in calculation we have taken the value of g as $10m/{{s}^{2}}$instead of $9.8m/{{s}^{2}}$
So, we have
\[\Rightarrow {{F}_{up}}=120N\]
Now,
Let the mass of the monkey which is coming down the rope be ${{m}_{2}}$
So, we have
${{m}_{2}}=8kg$
Also, the velocity of the monkey that is coming up is given to us,
v = $2m/s$
Since there is no acceleration, only the gravitational force will act on the monkey coming down
So, the forces acting on the rope due to the monkey coming down will be
\[{{F}_{Down}}={{m}_{2}}g\]
Now, using the give values
We have
\[\Rightarrow {{F}_{up}}=8\times 10\]
\[\Rightarrow {{F}_{up}}=80N\]
Now, net tension acting on the rope due to the movement of the two monkeys will be
${{T}_{Net}}={{F}_{up}}+{{F}_{Down}}$
${{T}_{Net}}=120N+80N$
${{T}_{Net}}=200N$

Note: In physics, tension is defined as a pulling force transmitted axially by a string, a cable, a cord, or related one - dimensional continuous material, or by each end of a rod. Its SI – Unit is Newton (N), named after the great mathematician and physicist Isaac Newton.