Duration: 2:49

47 views

0

A small block is connected to one end of a massless spring of unstretched length \( 4.9 \mathrm{~m} \). The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by \( 0.2 \mathrm{~m} \) and
\( \mathrm{P} \) released from rest at \( t=0 \). It then executes simple

W) harmonic motion with angular frequency \( \omega=\frac{\pi}{3} \mathrm{rad} / \mathrm{s} \).
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 \( 10 \mathrm{~m} \) from \( O \). If the pebble hits the block at \( t=1 \mathrm{~s} \), the value of \( v \) is (take, \( g=10 \mathrm{~m} / \mathrm{s}^{2} \) ) (2012)
(a) \( \sqrt{50} \mathrm{~m} / \mathrm{s} \)
(b) \( \sqrt{51} \mathrm{~m} / \mathrm{s} \)
(c) \( \sqrt{52} \mathrm{~m} / \mathrm{s} \)
(d) \( \sqrt{53} \mathrm{~m} / \mathrm{s} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live