Question

A smaller block of mass 'm' is placed on another block of mass M. When a horizontal force F is applied on the block of mass M as shown in the figure, the smaller block does not slide. If the magnitude of friction between the bigger block and ground is 'f' , determine the magnitude and direction of friction between the two blocks.

A
FM+m
B
FfM+m
C
F+fM+m
D
Ffm

Solution

The correct option is B $$\displaystyle\dfrac { F -f}{ M+m }$$Let a be the combined acceleration of both blocks.$$F - f_r = (m + M)a$$$$a=\cfrac{F - f_r}{ (m + M)}$$Now, consider FBD from fig. (2);$$f_b -$$ frictional force between the two blocks.$$f_b = ma$$ $$f_b = \cfrac{m(F - f_r)}{ (m + M)}$$the direction of friction is shown in fig.Physics

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