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Question

# Pulley - massless, frictionless String - massless Wedge-frictionless In the figure find the acceleration of the blocks if the wedge is fixed.

A

rightwards

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B

rightwards

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C

leftwards

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D

none of these

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Solution

## The correct option is C leftwards lets choose that the blocks will move right. So 5kg block will accelerate down the incline 10kg the incline. String is inextensible, so both will have same acceleration mg sinθ T - 10 × 10 × 12 = 10a T - 50 = 10a -------------------(i) 5g sin 45 - T = 5a 50(1√2)−T=5a ----------------(ii) solving (i) & (ii) We get a=103(1−√2√2) Well this is negative (∵√2>1).So math is telling us that the blocks will accelerate in the negative. direction or the opposite of the chosen direction Well let's check out how correct all the mathematics behind it is. Let's change the direction of chosen acceleration. 50 - T = 10a ----------------(iii) T = 50√2=5a ----------------(iv) Solving (iii) & (iv) we get a=103(√2−1√2) maths checks out Nice!!!

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