Match the combination of springs shown in Column 1 with their respective time periods in Column II.

Options

A. a-(i), b - (ii), c-(iv), d - (iii)
B. a- (iv), b, (iii), c-(i), d - (ii)
C. a-(iii), b -(i), c-(iv), d - (ii)
D. a-(i), b - (iii), c-(ii), d - (iv)

Answer

B

Explanation

In figure A, two springs are connected in parallel. The effective spring constant is, `k_(eff) = k_1 + k_2`
`:. T= 2pi sqrt(m/(k_1+k_2)), A-s`
In figure B, two identical spring are connected in parallel. The effective spring constant is
`k_(eff) = k = k = 2k :. T = 2pi sqrt(m/(2k)),B-r`
In figure C, two identical spring are connected in series. The effective spring constant is
`1/(k_(eff)) = 1/k_1 +1/k_2 = (k_2+k_1)/(k_1k_2) " or " k_(eff) =(k_1k_2)/(k_1+k_2)`
`:. T =2pi sqrt((m(k_1+k_2))/(k_1k_2)), C-p`
In figure D, two identical spring are connected in series. The effective spring constant is
`K_(eff) =((k)(k))/(k+k) =k/2 :. T= 2pi sqrt((2m)/k), D-q`