Physics Class 11th Work, Energy and Power

In a spring gun having spring constant 100N/m a small ball ‘B’ of mass 100g is put in its barrel (as shown in figure) by compressing the spring through 0.05m. 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 2m above the ground. The value of d is__________m.

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Answered by

alok kumar singh | Contributor-Level 10

a month ago

Let ball starts its motion with horizontal velocity v₀, so with the help of conservation of mechanical energy, we can write

$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m x^{2} \Rightarrow v_{0} = x \sqrt[]{\frac{k}{m}} = 0.05 \times \sqrt[]{\frac{100}{0.1}} = 0.5 \times \sqrt[]{10} m / s$

t = Time required to fall the ball = $\sqrt[]{\frac{2 h}{g}} = 2 \times \sqrt[]{\frac{1}{10}} s$

^{$= d = v_{0} \times t = 0.5 \times \sqrt[]{10} \times 2 \times \sqrt[]{\frac{1}{10}} = 1 m$}

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