A) \[7m/{{s}^{2}}\]downwards
B) \[2m/{{s}^{2}}\] downwards
C) \[10m/{{s}^{2}}\] downwards
D) \[8m/{{s}^{2}}\] downwards
Correct Answer: C
Solution :
[c] Taking upward direction as positive. Given \[{{a}_{A}}=1m/{{s}^{2}}\] \[{{a}_{B}}=7m/{{s}^{2}}\] and \[{{a}_{C}}=2m/{{s}^{2}}\] Let acceleration of pulley P is 'a' upwards, then acceleration of pulley Q will be 'a' downwards. or \[{{a}_{p}}=a\] and \[{{a}_{Q}}=-a\] Now \[{{a}_{AP}}=-{{a}_{BP}}\] or \[{{a}_{A}}-{{a}_{P}}={{a}_{P}}-{{a}_{B}}\] or \[1-a=a-7\] or \[2a=8\] or \[a=4m/{{s}^{2}}\] Further \[{{a}_{CQ}}=-{{a}_{DQ}}\] or \[{{a}_{C}}=-{{a}_{Q}}={{a}_{Q}}-{{a}_{D}}\] or \[2-(-a)=-a-{{a}_{D}}\] or \[{{a}_{D}}=-2a-2=-10m/{{s}^{2}}\] \[\therefore \] Acceleration of D is \[10\text{ }m/{{s}^{2}}\]downwards.
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