A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency `omega = (pi)/(3) `rad/s . Simultaneously at t = 0, a small pebble is projected with speed `nu` from point P at an angle of `45^(@)` as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1s, the value of `nu` is (take g = 10 m/`s^(2)` )

Options

A. `sqrt(50)` m/s
B. `sqrt(51)` m/s
C. `sqrt(52)` m/s
D. `sqrt(53)` m/s

Answer

C