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Standard XII

Physics

Relative Velocity

Three blocks ...

Question

Three blocks of masses $m_{1,} m_{2}$ , and $m_{3}$ are connected by a massless unstrechable string as shown in the figure on a frictionless table. They are pulled by a force $T_{3} = 40 N$ . If $m_{1} = 10 k g$ , $m_{2} = 6 k g$ and $m_{3} = 4 k g$ , then tension $T_{2}$ will be:

12 N

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18 N

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32 N

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44 N

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Solution

The correct option is B $32 N$
In this case, all the three blocks are constrained to move with the same acceleration $a$ .
$a = \frac{40}{10 + 6 + 4} = 2 m s^{- 2}$
Tension force $T_{2}$ acts as if it is pulling the blocks $m_{1}$ and $m_{2}$ with an acceleration of $2 m s^{- 2}$ .
$∴ T_{2} = (10 + 6) \times 2 = 32 N$

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