The force constants of two springs are`K_(1) and K_(2)`. Both are stretched till their elastic energies are equal. If the stretching forces are ` F_(1) and F_(2) then F_(1) : F_(2)` is

Options

A. `sqrt(K_(1)) : sqrt(K_(2))`
B. `K_(2) : K_(1)`
C. `K_(1)^(2) : K_(2)^(2)`
D. `K_(1) : K_(2)`

Answer

A

Explanation

The elastic energy of a spring `=(1)/(2)Kx^(2)`
"sin"ce their energies are equal, `(1)/(2)K_(1)x_(1)^(2)=(1)/(2)K_(2)x_(2)^(2)`
`therefore K_(1)x_(1)=K_(2)x_(2)^(2)`
But `because F=Kx`
`therefore x=(F)/(K) and x_(1)=(F_(1))/(K_(1)) and x_(2)=(F_(2))/(K_(2))`
`therefore K_(1)xx (F_(1)^(2))/(K_(1)^(2))=K_(2)xx(F_(2)^(2))/(K_(2)^(2))`
`therefore (F_(1)^(2))/(K_(1))=(F_(2)^(2))/(K_(2)) therefore (F_(1))/(F_(2))=sqrt((K_(1))/(K_(2)))`