A plank of mass 12 kg is supported by two identical springs as shown is Fig. The plank always remains horizontal. When the plank is pressed down and released it performs simple harmonic motion with time period 3 s. When a block of m is attached to the plank the time priod changes to 6 s. The mass of the block is

Options

A. 48 kg
B. 36 kg
C. 24 kg
D. 12 kg

Answer

B

Explanation

Let spring constant of each spring be k then the equivalent spring constant of the two spring system in parallel is 2k
Without mass, `T=3s=2pisqrt((12)/(2k))`
With mass, `T_1=65=2pisqrt((12+m)/(2k))`
`(T)/(T_1)=(1)/(2)=sqrt((12)/(12+m))`
`m=36kg`