All surfaces shown in the figure are assumed to be frictionless and the pulleys and the string are light.

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Solution

Q.
All surfaces shown in the figure are assumed to be frictionless and the pulleys and the string are light.

The acceleration of the block of mass 2 kg is [2024].

1 $g$

2 $\frac{g}{3}$

3 $\frac{g}{2}$

4 $\frac{g}{4}$

Ans.
(2)

By constrained motion

$- a_{1} + a_{2} + a_{2} = 0$

$a_{1} - 2 a_{2} = 0 or a_{2} = \frac{a_{1}}{2}$

$T - 2 g \sin 30 ° = 2 a_{1}$

$\Rightarrow T - g = 2 a_{1}$ ...(1)

$4 g - 2 T = 4 a_{2}$

$\Rightarrow 4 g - 2 T = 2 a_{1}$

$\Rightarrow 2 g - T = a_{1}$ ...(2)

Adding equation (1) and (2), $g = 3 a_{1} \Rightarrow a_{1} = \frac{g}{3}$

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