A load of mass 100 gm increases the length of wire by 10 cm. If the system is kept in oscillation, its time period is `(g=10m//s^(2))`

Explanation

Data : m = 100 g = `100 xx 10^(-3)` kg , x = 10 cm, = 0.1 m = g = 9.8 m/`s^(2)`
` m_(1) =400 g= 400 xx 10^(-3)` kg
(1) Stretching force F = mg
F = kx ( numerically) where k is the force contsant .
mg = kx
` k = (mg)/x= (100 xx 10^(-3) xx 9.8)/(0.1) = 9.8 ` N/m
The period , ` T = 2pi, sqrt(m/k) = 2xx 3.142 xx sqrt((0.1)/(9.8)) = 0.6348 s`
(2) ` T_(1) = 2pi sqrt(m_(1)/k)`
`T_(1)/T = sqrt(m_(1)/m,`
The new period , `T_(1) = T sqrt(m_(1)/m = 0.6348 xx sqrt((40 xx10^(-3))/(100 xx 10^(-3)))`
` = 0.6348 xx 2 = 1.2696 s`