A block A (5kg) rests over another block B (3kg) placed over a smooth horizontal surface. There is friction between A and B. A horizontal force `F_1` gradually increasing from zero to a maximum is supplied to A so that the blocks move together without relative motion. Instead of this another horizontal force `F_2`, gradually increasing from zero to a maximum is supplied to B so that the blocks move together without relative motion. Then

Options

A. `F_(1)( max)=F_(2)(max)`
B. `F_(1)(max) gt F_(2)(max)`
C. `F_(1)(max) lt F_(2)(max)`
D. `F_(1)(max) : F_(2)(max)=5:3`

Answer

B, D

Explanation

`(B,D)` Case `I:`
Since, no relative motion `:`
`a=(F_(1)-F_(f))/(5)=(F_(f))/(3)rArr F_(1(max))=(8)/(3)F_(f)`
Case `II:`
`a=(F_(f))/(5)=(F_(2)-F_(f))/(3)rArr F_(2(max))=(8)/(5)F_(f)`
Clearly , `F_(1(max))gtF_(2(max)) ` and `F_(1(max))/F_(2(max))=(5)/(3)`