Question

A block `A` of mass `m_(1)` rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block `B` of mass `m_(2)` is suspended. The coefficient of knetic friction between the block and table is `mu_(k)` . When the block `A` is sliding on the table, the tension in the string is.
A. `((m_(2) - mu_(k) m_(1)) g)/((m_(1) + m_(2)))`
B. `(m_(1) m_(2) (1 + mu_(k)) g)/((m_(1) + m_(2)))`
C. `(m_(1) m_(2) (1 - mu_(k)) g)/((m_(1) + m_(2)))`
D. `((m_(2) + mu_(k) m_(1)) g)/((m_(1) + m_(2)))`

Answer 1

`m_(2) g - T = m_(2) a`
`T - mu_(k) m_(1) g = m_(1) a`
(i)/(ii)
`(m_(2) g - T)/(T - mu_(k) m_(1) g) = (m_(2) a)/(m_(1) a) implies m_(1) m_(2) g - m_(1) T`
`= m_(2) T = mu_(k) m_(1) m_(2) g`
`T = (m_(1) m_(2) (1 + mu_(k)) g)/((m_(1) + m_(2)))`