A spring has a certain mass suspended from it and its period of vertical oscillations is T ₁ . The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now T ₂ . The ratio of T₂ / T₁ is

Step-by-step solution

aligned & T =2 ~m ~K ~T 1 ~K & ~T ₂ ~T ₁ = K ₁ ~K ₂ aligned ...(i) Let K be the spring constant of the spring cut in half. For series combination, K ₁= K K ~K + K = K 2 For second case, the mass is hung to only one half of the spring, K ₂= K Substituting in K ₁ and K ₂ in (i), T₂ T₁ = K / 2 K = 1 2