1.

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)?

Answer»

`(m_(2))/(m_(1))`
`1+(m_(2))/(m_(1))`
`(m_(1))/(m_(2))`
`1+(m_(1))/(m_(2))`

Solution :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))`.


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