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Consider the situation shown in figure. All the surfaces are smooth. The tension in the string connected to 2 m is

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$\frac{mg}{3}$

$\frac{4 mg}{3}$

$\frac{2 mg}{3}$

answer is C.

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Detailed Solution

$a_{A} = \frac{a_{B} + 0}{2}$

$2 a_{A} = a_{B}$

${ma}_{B} = m (2 a_{A})$ ------(i)

2T = 2m. $a_{A}$ ---------(ii)

From 2(i) + (ii), we get

2mg = 6m $a_{A}$

$T^{'} = 2 {ma}_{A} = \frac{2 mg}{3}$

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