An insect of mass `m` is initially at one end of a stick of length `L` and mass `M`, which rests on a smooth floor. The coefficientg of friction between the insect and the stick is k. The minimum time in which the insect can reach the other end of the stick is t. Then `t^(2)` is equal to

Options

A. `2L//kg`
B. `2Lm//kg(M+m)`
C. `2LM//kg(M+m)`
D. `2Lm//kgM`

Answer

C

Explanation

An insect …………..
Maximum froce of friction `= kmg`
`:.` maximum acceleration of insect `= a_(1) = (kmg)/(m) = kg`
and maximum acceleration of stick ` = a_(2) = (kmg)/(M)`
`:.` acceleration of insect with respect to stick
`= a=a_(1)-(-a_(2))=kg (1+(m)/(M))`
`:. L = (1)/(2)at^(2) or t^(2) = (2L)/(a) = (2ML)/(kg(M+m))`