Question

Four springs, having lengths in the ratio 1:2:3:4, are made from a given roll of wire of a given material. 

The time periods, of simple harmonic oscillations of a given mass M, when attached to a spring having a spring constant equivalent to the (i) series combination (ii) parallel combination, of these four springs, are T₁ and T₂ , respectively. The ratio (T₁/T₂) equals (nearly)

(1) 4.3

(2) 4.6

(3) 4.9

(4) 5.2

Answer 1

(2) 4.6

The spring constant (for same material and same area of cross section) can be taken as inversely proportional to the length of the spring. 

Hence the spring constants, of the four springs, may be taken as

For the series combination, the equivalent spring constant, say K₁ , in given by

For the parallel combination, the equivalent spring constant, say K₂ , is given by