Q 11-05-146JEE MainJEE Main 2021 (20 Jul, Shift 1)Easy
In a spring gun having spring constant $100\ \text{N m}^{-1}$ a small ball $B$ of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance $d$ on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of $d$ is ______ m.
($g = 10\ \text{m s}^{-2}$)
Numerical value type. Enter your answer.
Answer: 1
Launch speed: $\frac12kx^2 = \frac12mv^2 \Rightarrow v = x\sqrt{\dfrac km} = 0.05\sqrt{\dfrac{100}{0.1}} \approx 1.58$ m/s.
Time to fall 2 m: $t = \sqrt{\dfrac{2\times2}{10}} \approx 0.632$ s.
$d = vt \approx 1.58\times0.632 \approx 1$ m.
Solution by Sreeraj P, M.Sc Physics