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Tension in a String

Two blocks of...

Question

Two blocks of mass $5 k g$ and $3 k g$ are tied with a heavy rope of mass $2 k g$ . An external force of $200 N$ is applied on $5 k g$ block and the whole system accelerates upwards. Find the tension at the midpoint of the rope?
(Take $g = 10 m / s^{2}$ )

80 N

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100 N

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120 N

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60 N

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Solution

The correct option is A $80 N$
To calculate the total acceleration let us consider the entire setup to be a system of mass $(5 + 2 + 3) = 10 k g$
FBD of the system will be

Using FBD, we can write
$F - M g = M a$
$200 - 10 \times 10 = 10 \times a$
$a = 10 m / s^{2}$
The rope of mass $2 k g$ can be seen to be made up of two parts of $1 k g$ each, of equal length.
Now, the FBD of the lower part of the system will be

Using FBD, we can write $T - 4 \times g = 4 \times a$
$T - 4 \times 10 = 4 \times 10$
$⟹ T = 80 N$

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