A body has a time period (4/5) s under the action of one force and (3/5) s under the action of another force. Then time period when both the forces are acting in the same direction simultaneously will be

Options

A. `4//5 s`
B. `5//4 s`
C. `1 s`
D. `12//25 s`

Answer

D

Explanation

`F=F_(1)+F_(2)`
`T^(2)prop(1)/(F) therefore Fprop(1)/(T^(2))`
`T=(T_(1)T_(2))/(sqrt(T_(1)^(2)+T_(2)^(2)))=((4)/(5)xx(3)/(5))/(sqrt((16)/(25)+(9)/(25)))=(12//25)/(1)`
`therefore T=0.48`