Question

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 to = $\frac{\pi }{3}$ rad/s. Simultaneously at t = 0, a small pebble is
projected with speed v from point P at an angle of 45$^{\circ}$ as shown in
the figure.
Point P is at a horizontal distance of 10 m from O. If the pebble
hits the block at / = 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 1

Answer: (A)

t = time of flight of projectile
$ \, \, \, \, = \frac{ 2v sin \theta }{ g } \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, (\theta = 45 ^ \circ )$
$\therefore \, \, \, \, v= \frac{ gt}{ 2 sin \theta = \frac{ 10 \times 1}{ 2 \times 1/ \sqrt 2}}$
$ \, \, \, \, \, \, \, \, \, \, = \sqrt {50} m/s $