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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 (v) 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 = 1 s`, the value of (v) is `(take g = 10 m//s^2)`.
(##JMA_CHMO_C10_012_Q01##).

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 phojectile
`T = (2usintheta)/(g) = 1` sec.
`(2usin45)/(g) = 1` sec : `u = (g)/(sqrt(2)) : u = sqrt(50) m//s`
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