question_answer

Acceleration of each block is given as \[g/5\sqrt{2}\]. Find the magnitude and direction of force exerted by string on pulley.

A)  6 mg/5, downward direction

B)  6 mg/5, upward direction

C)  6 mg/5, horizontal direction

D)  Not possible to have acceleration

Correct Answer: A

Solution :

Let coefficient of friction be u. and 3m block is moving down the incline, then Acceleration \[=\frac{\text{net pulling force}~~~}{\text{total mass}}\] \[a=\frac{3mg\sin {{45}^{o}}-3\mu mg\cos {{45}^{o}}-mg\sin {{45}^{o}}}{4m}\] \[=\frac{(2-3\mu )g}{4\sqrt{3}}\] \[=\frac{(2-1.2)g}{4\sqrt{2}}=\frac{g}{5\sqrt{2}}\]                             \[(\because \mu =0.4)\] \[\Rightarrow \] \[T=6mg/(5\sqrt{2})\] Force exerted by string/on pulley is \[\sqrt{2}T\]as shown in figure.      \[\therefore \,\,\,\,F=\frac{6mg}{5}.\]