Q. A $15\ g$ ball is shot from a spring gun whose spring has a force constant of $600\ N/m.$ The spring is compressed by 5 $cm.$ The greatest possible horizontal range of the ball for this compression is ($g = 10\ m/s^{2}$)
A) $6.0\ m$
B) $10.0\ m$
C) $12.0\ m$
D) $8.0\ m$
Explanation
(b) For getting horizontal range, there must be some inclination of spring with ground to project ball
$\Rightarrow R_{\max} = \frac{u^{2}}{g}\ \ \ \ $ …(i)
But K.E. acquired by ball = P.E. of spring gun
$\Rightarrow \frac{1}{2}mu^{2} = \frac{1}{2}kx^{2} \Rightarrow u^{2} = \frac{kx^{2}}{m}\ \ \ \ \ \ldots(ii)$
From equation (i) and (ii)
$R_{\max} = \frac{kx^{2}}{mg} = \frac{600 \times \left( 5 \times 10^{- 2} \right)^{2}}{15 \times 10^{- 3} \times 10} = 10m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.