The correct option is C Maximum speed of block is 2g√mk
When block is released, the spring will stretch by x and block will move downwards by 2x.
By energy conservation principle,
Energy gain by spring = Loss in gravitational potential energy by block
⇒xmax=4mgk ( at maximum elongation)
The block will attain maximum velocity when net force on the pulley is zero.
Let net force on block be zero when x=x′
At equilibrium, kx′=2mg
The kinetic energy of the block is given by
Substituting x′ to get maximum velocity (vmax)
Hence, options (a) and (c) are the correct answers.