Two identical particle each of mass `m` are inter connects by a light spring of stiffness `k` ,the time period for small oscillation is equal to

Options

A. `2pi sqrt((m)/(k))`
B. `(pi)/(2) sqrt((m)/(k))`
C. `pi sqrt((m)/(2k))`
D. `pi sqrt((2m)/(k))`

Answer

D

Explanation

The reduced mean
`mu = ((m)(m))/(m + m) = (m)/(2)`
The given system is equavalent to a system at a particle of mass `m` ? Connected to a spring of stiffness `k` rigidly.
The requred period of osciltion
`T = 2pi sqrt((mu)/(k)) = 2pi sqrt((m//2)/(k))`
`= pisqrt((2m)/(k))`