First slide

Constraints

Question

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

Moderate

A

$\frac{mg}{3}$
B

$\frac{4 mg}{3}$
C

$\frac{2 mg}{3}$
D

mg

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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