A `15 gm` ball is shot from a spring whose spring has a force constant of `600 N//m`. The spring is compressed by `5 cm`. The greater possible horizontal range of the ball for this compression is

Options

A. `6.0 m`
B. `12.0 m`
C. `10.0 m`
D. `8.0 m`

Answer

B

Explanation

`R_(max) = (u^(2))/(g) at theta = 45^(@)`
`R_(max) = ((m u^(2))/(2)) ((2)/(mg)) = ((1)/(2) kx^(2)) ((2)/(mg))`
As `((1)/(2) m u^(2) = (1)/(2)kx^(2)) ((2)/(mg))`
As `((1)/(2) m u^(2) = (1)/(2) kx^(2)) implies R_(max) = (kx^(2))/(mg)`
Substituting the values
`R_(max) = ((600) (5 xx 10^(-2))^(2))/((15 xx 10^(-3)) (10)) = 10.0m`