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 )

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

Tardigrade Admin · Accepted Answer

Here, Rmax = (u2/g) = (1/2)mu2 × (2/mg) But (1/2) mu2 = (1/2)kx2 ∴ Rmax = (1/2)kx2×(2/mg) = (kx2/mg) = (600 × (0.05)2/0.015 × 10) = 10 m

Q. 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 $5 c m$ . The greatest possible horizontal range of the ball for this compression (Take $E = 10 m s^{- 2}$ )

$6 m$

$8 m$

$10 m$

$12 m$

Here, $R_{ma x} = \frac{u ^{2}}{g} = \frac{1}{2} m u^{2} \times \frac{2}{m g}$
But $\frac{1}{2} m u^{2} = \frac{1}{2} k x^{2}$
$∴ R_{ma x} = \frac{1}{2} k x^{2} \times \frac{2}{m g}$
$= \frac{k x ^{2}}{m g} = \frac{600 \times ( 0.05 ) ^{2}}{0.015 \times 10} = 10 m$

Q. A 15g ball is shot from a spring gun whose spring has a force constant 600Nm−1 . The spring is compressed by 5cm . The greatest possible horizontal range of the ball for this compression (Take E=10ms−2 )

6m

8m

10m

12m