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 A 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 ) `

Answer

C

Explanation

`T_(1)=2pisqrt((M)/(k_(1))) or k_(1)=(4pi^(2)M)/(T_(1)^(2))` and `k_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))`
`thereforeT=2pi sqrt((M)/(k_("eff")))=sqrt(T_(1)^(2)+T_(2)^2)`