A gun applies a force F on a bullet which is given by `F=(100-0.5xx10^(5)t)N`. The bullet emerges out with speed 400 m/s. then find out the impulsive exerted till force on bullet becomes zero.

Options

A. 0.2N-s
B. 0.3N-s
C. 0.1N-s
D. 0.4N-s

Answer

C

Explanation

`F=(100-0.5xx10^(5)t)N`
Given F=0
`100-0.5xx10^(5)t=0`
`100=0.5xx10^(5)t`
`T=2xx10^(-3)`sec
`I=intFdt`
`I=underset(0)overrset(2xx10^(-3))int(100-0.5xx10^(5)t)dt`
`I=[100t-(10^(5))/(2)(t^(2))/(2)]_(0)^(2xx10^(-3)`
`I=[100xx2xx10^(-3)-(10^(5))/(4)xx4xx10^(-6)]`
`I=[2xx10^(-1)-10^(-1)]`
`I=10^(-1)=0.1N-s`