Three mass 0.1 kg ,0.3 kg and 0.4 kg are suspended at end of a spring. When is 0.4 kg mass is removed , the system oscillates with a period 2 s . When the 0.3 kg mass is also removed , the system will oscillates with a period

Options

A. 1 s
B. 2s
C. 3 s
D. 4 s

Answer

A

Explanation

Original mass =0.1+0.3+0.4=0.8 kg
When the 0.4 kg mass is removed, the remaining mass =0.4 kg
`therefore T_(1)=2pi sqrt((m_(1)+m_(2))/(K)) therefore 2 = 2pi sqrt((0.4)/(K))`
When 0.3 kg mass is removed, then remaining mass =0.1 kg
`therefore T_(2)=2pi sqrt((0.1)/(K))`
`therefore` Dividing (2) by (1), we get
`therefore (T_(2))/(2)=sqrt((0.1)/(0.4))=(1)/(2) therefore T_(2)=T_(1)s`