A tray of mass M = 10 kg executes SHM of period 1.5s. It is supported on two identical springs of spring constant k as shown in figure. If a block of mass m is also placed on the tray, the period of oscillation increases to 3s. The value of m is:

Options

A. 10 kg
B. 20 kg
C. 30 kg
D. 40 kg

Answer

C

Explanation

As the two identical springs are connected in parallel,
`therefore` The effective spring constant of the combination is:
`k. = k + k = 2k`
`therefore T = 2pi sqrt(M/k^(.)) = 2pi sqrt(M/(2k))`......... (i)
When a block of mass m is placed in the tray, the period of oscillation becomes
`T. = 2pi sqrt((M+m)/(k.)) = 2pi sqrt((M+m)/(2k))`.......... (ii)
Divide (ii) by (i), we get:
`T/T = sqrt((M+m)/M)`
`3/1.5 = sqrt((10 + m)/10)`
Squaring both sides, we get:
`4 = (10 + m)/10` or `40 = 10 + m` or `m 30` kg