Block A has mass `40 kg` and B has `15 kg` and F is `500N` parallel to smooth inclined plane.The system is moving together

The least coefficient of friction between A and B is

Options

A. `(5sqrt(2))/(12)`
B. `(9sqrt(3))/(53)`
C. `(9sqrt(2))/(28)`
D. `(5sqrt(3))/(18)`

Answer

B

Explanation

`500 - 55 g sin 30^(@)= 55a rArr a= (45)/(11) ms^(-2)`

`N - 15g = 15a sin30^(@)`
`N = 15[10 +(45)/(11)xx(1)/(2)]= (265 xx 15)/(22)`
`f = 15a cos 30^(@)= 15 xx(45)/(11)(sqrt(3))/(2)`
For A not as slide B` fle f_(1)`
`rArr (15 xx45)/(11) xx sqrt(3)/(2) le mu((265 xx 15)/(22)) rArr m ge (9sqrt(3))/(53) = 0.294`