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Two blocks of masses 50 Kg  and 30 Kg  connected by a massless string pass over a tight frictionless , pulley and rest on two smooth planes inclined at angles 30 \degree  nad 60 \degree  reaspectively with horizontal as shown in the figure .If the system is released from rest then find time taken by 30 Kg block to reach the ground 

Answers (2)

@Anupam

here is the figure and solution

 

 T - 50g \sin 30 = 50a ....(1) \\ 30 g \sin 60 - T = 30 a .....(2)

Adding (1)  and (2) 

a = \frac{30g \sin 60 - 50g \sin 30 }{80 } = 0.12 m /s

Now s = ut + 1/2 at^2 \\ 6 = 1/2 \times 0+(1/2)*0.12 \times t^2 \\ t^2 = \frac{6 \times 2}{0.12} = 100 \\ t = 10 sec

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