In the arrangement shown in figure pulley and strings are ideal. End $A$ of string connected to pulley $P_{1}$ is moved upwards with acceleration $a_{A} = 2 m / s^{2}$ while end $B$ of another string shown in figure is moved up with acceleration $a_{B} = 1 m / s^{2}$ . Block $C$ of mass $1 k g$ is moving up with acceleration $1 m / s^{2}$ . If block $D$ to which string are connected symmetrically moves such that its orientations remains same then (assume $g = 10 m / s$ )

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acceleration of block $D$ is $1 / 2 m / s^{2}$ upwards

mass of block $B$ is $1 / 2 k g$

end $A$ is pulled with force of $22 N$

acceleration of block $B$ is $7 / 3 m / s^{2}$ upwards

answer is B, D.

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Detailed Solution

$(b, d)$ By constraint

$a_{B} + 4 a_{A} = 2 a_{C} + 3 a_{D} \Rightarrow a_{D} = \frac{7}{3} m / s^{2}$

$2 T - 10 = 1 \Rightarrow T = 11 / 2 N$

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