A body of mass `m_1=4` kg moves at `5 hati m//s` and another body of mass `m_2=2` kg moves at `10 hati m//s`. The kinetic energy of center of mass is

Options

A. `200/3J`
B. ` 500/3J`
C. `400/3J`
D. `800/3J`

Explanation

Acceleration on a rough inclined plane,
`a_1=gsintheta=gsin45^0`
Acceleration on a smooth inclined plane,
`a_2=gsintheta-mu_(kg)costheta=gsin45^0 -mu_k cos45^0=g/sqrt2(1-mu_k)`
`aprop1/(t^2)`
`implies(t_1^2)/(t_2^2)=(a_2)/(a_1)=[g/sqrt2(1-mu_k)]/(g/sqrt2)=1-mu_k`
`impliest_1^2/t_2^2=1-mu_k ("or") 1-mu_k=1/n^2`
`mu_k=1-1/n^2`