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A small block is connected to one end of...

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)` )

A

` sqrt(50) m//s`

B

`sqrt(51) m//s`

C

`sqrt(52) m//s`

D

`sqrt(53) m //s`

Text Solution

Verified by Experts

The correct Answer is:
A
Time of flight for projectile
`T = (2 u sin 45^(@))/( g) ` = 1 sec
`rArr (2 u sin 45^(@))/( g) ` = 1 sec
`u = (g)/( sqrt( 2)) rArr u = sqrt(50) m//s `
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