JEE (Advanced) 2012 Paper-1 Question 5

Question 5

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 thefigure)is fixed. The system lies on a horizontal frictionless surface. The blockis stretched by 0.2 m and released from rest at t= 0. It then executes simple harmonic motion with angular frequency $$\omega = \frac{\pi}{3}$$ rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of $$45^\circ$$ as shownin thefigure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at + = 1s, the value of v is (take g = 10 $$m/s^2$$)

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