The time period of a spring-mass system is T . If this spring is cut into two parts, whose lengths are in the ratio 1 : 2 , and the same mass is attached to the longer part, the new time period will be

Step-by-step solution

The spring-mass system oscillates in SHM. Its time period is given by T = 2 π m k When spring is cut in ratio 1 : 2 , the new spring constant is k ' = 3 k ​/2 (for the longer part) ∴ T T ' = 3 k 2 k ⇒ T ' = 2 3 T