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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. 
401121.JPG


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


976788_401121_ans_8aa3eee3081046eca447250124743476.png

Physics

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