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 opposite direction simultaneously will be

Options

A. `4//5 s`
B. `5//4 s`
C. 1 s
D. `12//5 sqrt(7) 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))/((7)/(25))=(12)/(7)`