question_answer

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/s2)                    [DPMT 2004]

A)            6.0 m                                       

B)            10.0 m

C)            12.0 m                                     

D)            8.0 m

Correct Answer: B

Solution :

                   For getting horizontal range, there must be some inclination of spring with ground to project ball.      Þ \[{{R}_{max}}=\frac{{{u}^{2}}}{g}\]                                                                    ?..(i)                    But K.E. acquired by ball   = P.E. of spring gun                    \[\Rightarrow \frac{1}{2}m{{u}^{2}}=\frac{1}{2}k{{x}^{2}}\] Þ \[{{u}^{2}}=\frac{k{{x}^{2}}}{m}\]            ?..(ii)                    From equation (i) and (ii)            \[{{R}_{max}}=\frac{k{{x}^{2}}}{mg}\]\[=\frac{600\times {{(5\times {{10}^{-2}})}^{2}}}{15\times {{10}^{-3}}\times 10}\]=10m.