A mass m, connected to a horizontal spring performs SHM with amplitude A. While mass m, is passing through mean position, another mass m, is placed on it so that both the masses move together with amplitude A,. The ratio of

Options

A. `[m_1/(m_1+m_2)]^(1/2)`
B. `[(m_1+m_2)/m_1]^(1/2)`
C. `[m_2/(m_1+m_2)]^(1/2)`
D. `[(m_1+m_2)/m_2]^(1/2)`

Answer

A

Explanation

Potential energy of oscillating mass is given by `PE=1/2kx^2`
When only one block is oscillating at x=A
`E_("max")=1/2KA^2` and at mean position x=0. So, E=0
`therefore A alpha 1/sqrtm`
When mass `m_(2)` is placed on top of the mass m. Then, total mass is `(m_1 + m_2)` and E=0 at this point, as x = 0. lt brgt When they reaches at x = A,
When they reaches at x = A,
then `A_1prop 1/sqrt(m_1+m_2)`
Dividing Eq. (ii) by Eq. (i),
`A_1/A=((m_1)/(m_1+m_2))^(1/2)`