Let `T_(1) and T_(2)` be the periods of springs A and B when mass M is suspended from one end of each spring. If both springs are taken in series and the same mass M is, suspended from the séries combination, the time period is T, then

Options

A. `T=T_(1)+T_(2)`
B. `(1)/(T)=(1)/(T_(1))+(1)/(T_(2))`
C. `T^(2)=T_(1)^(2)+T_(2)^(2)`
D. `(1)/(T^(2))=(1)/(T_(1)^(2))+(1)/(T_(2)^(2))`

Answer

D

Explanation

`T_(1)=2pisqrt((M)/(k_(1)))ork_(1)=(4pi^(2)M)/(T_(1)^(2))`
and `T_(2)=2pisqrt((M)/(k_(2)))ork_(2)=(4pi^(2)M)/(T_(2)^(2))`
In series combination, `k_(eff)=(k_(1)k_(2))/(k_(1)+k_(2))=(4pi^(2)M)/(T_(1)^(2)+T_(2)^(2))`
`therefore T=2pisqrt((M)/(k_(eff)))=sqrt(T_(1)^(2)+T_(2)^(2))orT^(2)=T_(1)^(2)+T_(2)^(2)`