A mass 'M' is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of period T . If the mass is increased by 'm&#

Question

A mass 'M' is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of period T . If the mass is increased by 'm', the time period becomes 3 5 T ′ ​ . What is the ratio ( m M ​ ) ?

TestHub · Accepted Answer

T = 2 π k M ​ ​ ; 3 5 T ​ = 2 π k M + m ​ ​ ∴ 3 5 ​ × 2 π k M ​ ​ = 2 π k M + m ​ ​ ∴ 9 25 ​ ⋅ k M ​ = k M + m ​ ∴ 9 25 ​ M = M + m Dividing by M , 9 25 ​ = 1 + M m ​ ∴ M m ​ = 9 25 ​ − 1 = 9 16 ​ m M ​ = 16 9 ​

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