Figure shows two block `A` and `B`, each having a mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block `A` can slide is smooth. The block `A` is attached to spring constant `40 N//m` whose other end is fixed to a support 40 cm above the horizontal surface. Initially, the spring is vertical and unstretched when the system is released to move. Find the velocity of the block A at the instant it breaks off the surface below it. Take `g = 10 m//s^(2)` .

Options

A. `sqrt((19)/(8))`
B. `sqrt((3)/(2))`
C. `sqrt((9)/(4))`
D. None of these

Answer

A

Explanation

When block A breaks off it has moved 0.3 m by energy conservation
`0.32 g 0.3 - 20 (0.01) + 0.32 v_(2)`
therefore `v = sqrt((19)/(8))`