A block A of m ass rests on a horizontal table. A lig h t strin g connected to it passesover a frictionless pulley at the edge of table an d from its other end another block B of mass `m_(2)` is su sp en d e d . The co efficien t of k in eticfriction between the block and the table is `mu_(k)` hen the block A is sliding on the table, the ten sio n in the string i s :

Options

A. `(m_(2)-mu_(k)m_(1)g)/(m_(1)+m_(2))`
B. `(m_(1)mu_(2)m(1+mu_(k))g)/(m_(1)+m_(2))`
C. `(m_(1)mu_(2)m(1-mu_(k))g)/(m_(1)+m_(2))`
D. `(m_(2)+mu_(k)m_(1)g)/(m_(1)+m_(2))`

Answer

B

Explanation

For the motion of both blocks
`m_(2) g - T -m_(2) a`
`T-mu_(2) m_(1) g = m_(1) a`
`rArr a= ((m_(2) -mu_(k) m_(1))g)/( m_(1) + m_(2))`

For the block on mass `m_(2)`
`m_(2) g - T = m_(2) [(m_(2) - mu_(k) m_(1))/(m_(1) +m_(2))] g`
`rArr = (m_(1)m_(2)(1+mu_(k))g)/( m_(1) +m_(2))`