1) A small block is connected to one end of a massless spring of unstretched 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 $\omega=\frac{\pi}{3}rad/s$. simultaneously at t=0, a small pebble is projected with speed v from point P at an angle of $45^{0}$ 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 $g=10 m/s^{2})$ A) $\sqrt{50}$ m/s B) $\sqrt{51}$ m/s C) $\sqrt{52}$ m/s D) $\sqrt{53}$ m/s Answer: Option AExplanation:t= tiime of flight of projectile $=\frac{2 v \sin \theta}{g}$ ($\theta=45^{0})$ $\therefore$ $v= \frac{gt}{2 \sin \theta}=\frac{10 \times 1}{2 \times 1/\sqrt{2}}=$ $\sqrt{50}$ m/s
