In the figure shown all the surface are smooth. All the blocks $A, B$ and $C$ are movable, x -axis is horizontal and $y$ -axis vertical as shown. Just after the system is released from the position as shown.

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N 1 ​ = ( N 2 ​ + M g ) cos θ ( N 2 ​ + M g ) sin θ = M a 1 ​ N 2 ​ + M a 1 ​ sin θ = M g M a 1 ​ cos θ = M a 2 ​ N 2 ​ = M g − M a 1 ​ sin θ ( 2 m g − m a 1 ​ sin θ ) sin θ = m a 1 ​ ( 2 g − a 1 ​ sin θ ) sin θ = a 1 ​ 2 g sin θ = ( 1 + sin 2 θ ) a 1 ​ a 1 ​ = 1 + s i n 2 θ 2 g s i n θ ​ a 1 ​ sin θ = 1 + s i n 2 θ 2 g s i n 2 θ ​

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JEE Main + Advanced (1 year 12th class)