Three blocks of masses m_1, m_2 and m_3 ar

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Three blocks of masses ${m_1},\,{m_2}$ and ${m_3}$ are connected by massless strings as shown on a frictionless table. They are pulled with a force ${T_3} = 40\,N$. If ${m_1} = 10\,kg,\,{m_2} = 6\,kg$ and ${m_3} = 4\,kg$, the tension ${T_2}$ will be ........ $N$

A

$20$

B

$40$

C

$10 $

D

$32$

Three blocks of masses ${m_1},\,{m_2}$ and ${m_3}$ are connected by massless strings as shown on a frictionless table. They are pulled with a force ${T_3} = 40\,N$. If ${m_1} = 10\,kg,\,{m_2} = 6\,kg$ and ${m_3} = 4\,kg$, the tension ${T_2}$ will be ........ $N$

${T_2} = ({m_1} + {m_2}) \times \frac{{{T_3}}}{{{m_1} + {m_2} + {m_3}}} = \frac{{(10 + 6) \times 40}}{{20}}$$ = 32\;N$