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

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_(l)`
Clearly
`F_(1(max)) gt F_(2 (max))` and `(F_(1(max)))/(F_(2(max)))=(5)/(3)`