A block of mass `m_(2)` is placed on a horizontal table and another block of mass `m_(1)` is placed on top of it. An increasing horizontal force F = at is exerted on the upper block but the lower block never moves as a result. If the coefficient of friction between the blocks is `μ_(1)` and that between the lower block and the table is `μ_(2)`, then what is the maximum possible value of `μ_(1)//μ_(2)`?

Options

A. `(m_(2))/(m_(1))`
B. `1+(m_(2))/(m_(1))`
C. `(m_(1))/(m_(2))`
D. `1+(m_(1))/(m_(2))`

Answer

B

Explanation

Let `f_(1)` be the frictional force acting between lower block and the upper block andf2 be the friction force acting between lower block and the table.
As `m_(2)` never moves, so friction acting in between the blocks is always less than or equal to friction acting between lower block and table.
`thereforef_(1)lef_(2)`
or `mu_(1)m_(1)glemu_(2)(m_(1)+m_(2))g`
or `(mu_(1))/(mu_(2))le(m_(1)+m_(2))/(m_(1))`
`rArr(mu_(1))/(mu_(2))le1+(m_(2))/(m_(1))`
So, maximum possible value of `(mu_(1))/(mu_(2))=1+(m_(2))/(m_(1))`.