In a spring gun having spring constant 100 N/m a small ball 'B' of… | JEE Main 2021 (20 Jul, Shift 1)

Q17JEE Main 2021 · 20 JUL · SHIFT 1Medium

Spring & Elastic Energy

In a spring gun having spring constant 100 N/m 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 m/s2).

Numerical answer type. Work it out, then open the answer.

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Answer: 1

Launch speed: $\frac{1}{2}kx^2 = \frac{1}{2}mv^2 \Rightarrow v = x\sqrt{k/m} = 0.05\sqrt{1000} \approx 1.58$ m/s
Time to fall 2 m: $t = \sqrt{\frac{2H}{g}} = \sqrt{0.4} \approx 0.632$ s
$d = vt = 1.58 \times 0.632 \approx 1$ m
So $d = 1$ m.

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