A tray of mass M=10kg is supported on two identical springs, each of spring constant k, as shown in figure, when the tray is depressed a little and released, it executes simple harmonic motion of period 1.5 s. when a blockof mass m is placed on the tray, the speed of oscillation becomes 3 s. the value of m is

Options

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

Answer

C

Explanation

There are two identical springs which are connected in parallel, ltBrgt `therefore` The effective spring consistant of the combination is
`k'=k+k=2k`
`therefore` Time period
`T=2pisqrt((M)/(k'))=2pisqrt((M)/(2k))` . . . (i)
when block of mass m is placed in the tray, the period of oscillation becomes
`T'=2pisqrt((M+m)/(k'))=2pisqrt((M+m)/(2k))` . . . (ii)
Divide (ii) by (i), we get
`(T')/(T)=sqrt((M+m)/(M))implies(3)/(1.5)=sqrt((10+m)/(10))`
On squaring both sides, we get
`4=(10+m)/(10)` or `40=10+m`
or m=30 kg.