46. A small block is connected to o...

46. 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 (Fig.)is fixed. The system lies on a horizontal friction less 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 w = rad/s. simultaneously, at t=0, a small pebble is projected with speed y from point P at an angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from 0. If the pebble hits the block at t = 1 s, the value of v is ( take g=10 m/s2) 100 m 5 m (a) V50 m/s (c) V52 m/s (b) V51 m/s (d) V53 m/s

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( begin{aligned} t &=text { time of flight of projectile } t &=frac{2 v sin theta}{g}left(0=45^{circ}right) therefore v=frac{g t}{2 sin theta} &=frac{10 times 1}{2 times frac{1}{sqrt{2}}} &=sqrt{50} mathrm{m} / mathrm{s} end{aligned} )
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