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Question

What is the maximum value of the force F such that the block shown in the arrangement, does not move? 
42934.jpg


A
20 N
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B
10 N
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C
12 N
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D
15 N
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Solution

The correct option is A 20 N
Maximum value of force applied is equal to its static friction force.
Here, friction force is $$f=\mu N$$
Here, normal reaction force is : $$N=Fsin{ 60 }^{ 0 }+mg$$
Let us balance the force applied in horizontal direction with frictional force
$$Fcos{ 60 }^{ 0 }=\mu (Fsin{ 60 }^{ 0 }+mg)\\ \dfrac { F }{ 2 } =\dfrac { 1 }{ 2\sqrt { 3 }  } \left( \dfrac { \sqrt { 3 } F }{ 2 } +\sqrt { 3 } \times 10 \right) $$

We get: $$F=\dfrac { F }{ 2 } +10\\ F=20N$$

Physics

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