A spring gun of spring constant `90 N cm^(-1)` is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, the velocity of the ball is 

Options

A. `50 m s^(-1)`
B. `40 ms^(-1)`
C. `60 m s^(-1)`
D. `90 ms^(-1)`

Answer

D

Explanation

Here , `m = 16 g = 16 xx 10^(-3) kg`
`k = 90 N cm^(-1) = 90 xx 10 Nm^(-1)`
`x = 12 cm = 12 xx 10^(-2) m`
According to the law of conservation of energy,
`1/2 mv^2 = 1/2 kx^2 " or " v^2 = (kx^2)/(m)`
or `v = xsqrt(k/m) (12 xx 10^(-2)m) sqrt((90 xx 100 Nm^(-1))/(16 xx 10^(-3) kg)) = 90 ms^(-1)`.
Thus the velocity of the ball `90 ms^(-1)`.