A system is shown in the figure. The force The time period for small oscilations of the two blocks will be

Options

A. `2pi sqrt((3m)/(K))`
B. `2pi sqrt((3m)/(2K))`
C. `2pi sqrt((3m)/(4K))`
D. `2pi sqrt((3m)/(8K))`

Answer

C

Explanation

Both the spring are in series
`:. K_(eq) = (K(2k))/(K +2K) = (2K)/(3)`
Time period
`T = 2pi sqrt((mu)/(K_(eq))) "where" mu = (m_(1) m_(2))/(m_(1) + m_(2))`
Here `mu = (m)/(2)`
`:. T = 2pi sqrt((m)/(2).(3)/(2K)) = 2pi sqrt((3m)/(4K))`.