Question

A $ 15 \,g $ ball is shot from a spring gun whose spring has a force constant $ 600\,N \,m^{-1} $ . The spring is compressed by $ 5\, cm $ . The greatest possible horizontal range of the ball for this compression (Take $ E = 10\,ms^{-2} $ )

• A. $ 6\,m $
• B. $ 8\,m $
• C. $ 10\,m $
• D. $ 12\,m $

Answer 1

Answer: (C)

Here, $ R_{max} = \frac{u^{2}}{g} = \frac{1}{2}mu^{2} \times \frac{2}{mg} $
But $ \frac{1}{2} mu^{2} = \frac{1}{2}kx^{2} $
$ \therefore R_{max} = \frac{1}{2}kx^{2}\times\frac{2}{mg} $
$ = \frac{kx^{2}}{mg} = \frac{600 \times \left(0.05\right)^{2}}{0.015 \times 10} = 10\,m $