Q11 of 42 Page 31

In Fig. 5.1, the co-efficient of friction between the floor and the body B is 0.1. The co-efficient of friction between the bodies B and A is 0.2. A force F is applied as shown on B. The mass of A is m/2 and of B is m. Which of the following statements are true?


We have given Let acceleration in body A and B is ‘a’.

Body A will move along with body B by force F till the force of friction between surface of A and B is larger or equal to zero.



Now taking system A+B then acceleration will be


⇒


⇒


⇒


So force on A


⇒ FAB


⇒FAB


⇒FAB


If FABis equal or smaller than f2 then body A will move along with body B.


So f2=FAB or


…(i)


N=Reaction force by B on A



[N₂=Normal reaction on B along with A by surface]


…. (ii)


From (i)


so adding this with equation (ii) we can say F …(iii)


F = 0.45mg Newton is the maximum force on B. so that A and B can move together. So option (e) is correct.


Both bodies can move together if F is less than or equal to 0.45mg Newton.


So options (a) and (b) are also correct and rejects the option (c) as 0.5mg>0.45mg.


For option (d): Minimum force which can move A and B together


⇒Fmin


⇒Fmin


⇒Fmin


Given force in option (d) 0.1mg Newton <0.25mg Newton. So body A and B will not move i.e.


Bodies A and B will remain in rest hence option (d) is also correct.

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