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. [2012]

Question

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 $ω = \frac{π}{3} rad/s .$ 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 $g = 10 {m/s}^{2}$ ) [2012]

Smart Achievers · Accepted Answer

(1)

Here, we don't need to consider the SHM part rather we will focus on projectile part only. Since the pebble hits the block after 1 sec. We can easily calculate the speed of projection (V) from this time of flight.

Time of flight of projectile,

$T = \frac{2 V \sin θ}{g}$

$∴$ $1 = \frac{2 V \sin 45 °}{g}$

$∴$ $V = \sqrt{50} {ms}^{- 1}$

Hence pebble is projected with a speed $V = \sqrt{50} {ms}^{- 1}$

Solution

1 $\sqrt{50} m/s$

2 $\sqrt{51} m/s$

3 $\sqrt{52} m/s$

4 $\sqrt{53} m/s$

Want Us to Email you About Special Offers & Updates?

Solution

1 50 m/s

2 51 m/s

3 52 m/s

4 53 m/s

Want Us to Email you About Special Offers & Updates?

1 $\sqrt{50} m/s$

2 $\sqrt{51} m/s$

3 $\sqrt{52} m/s$

4 $\sqrt{53} m/s$