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Applying NLM along 3 Axis

Three bodies ...

Question

Three bodies are lying on a frictionless horizontal table and these are connected by inextinsible and massless strings as shown in the figure. They are pulled towards right with a force $T_{3} = 60 N$ . If $m_{1}, m_{2}$ and $m_{3}$ are equal to 10 kg, 20 kg and 30 kg respectively, then the values of $T_{1}$ and $T_{2}$ will be

10 N, 10 N

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30 N, 10 N

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10 N, 30 N

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30 N, 30 N

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Solution

The correct option is C 10 N, 30 N
Given : $T_{3} = 60 N$ , $m_{1} = 10$ kg, $m_{2} = 20$ kg and $m_{3} = 30$ kg
For case 1:
Consider a system of mass $M_{T} = m_{1} + m_{2} + m_{3}$ is moving with acceleration $a$ .
$∴$ $M_{T} a = T_{3}$ ,
where $a$ , acceleration of the system and $M_{T} = m_{1} + m_{2} + m_{3}$
$⟹$ $a = \frac{T_{3}}{m_{1} + m_{2} + m_{3}} = \frac{60}{10 + 20 + 30} = 1 m / s^{2}$
For case-2:
A system of mass $m_{1} + m_{2}$ is moving with acceleration $a$ .
$∴$ $T_{2} = (m_{1} + m_{2}) a = (10 + 20) (1) = 30 N$
For case-3:
A block of mass $m_{1}$ is moving with acceleration $a$ .
$∴$ $T_{1} = m_{1} a = (10) (1) = 10 N$

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Three bodies are lying on a frictionless horizontal table and these are connected by inextinsible and massless strings as shown in the figure. They are pulled towards right with a force T3=60 N. If m1,m2 and m3 are equal to 10 kg, 20 kg and 30 kg respectively, then the values of T1 and T2 will be