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A cube of \[10N\] rests on a rough inclined plane of slope \[3\] in \[5\]. The coefficient of friction is \[0.6\]. The minimum force necessary to start the cube moving up the plane is:
A) $8.8{\text{N}}$
B) ${\text{16}}{\text{.2N}}$
C) ${\text{10}}{\text{.8N}}$
D) ${\text{21}}{\text{.6N}}$

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Last updated date: 01st Mar 2024
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IVSAT 2024
Answer
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Hint: Friction: It is defined as the opposing force acting on a body due to the presence of another body in contact when they are in motion.
Coefficient of friction: It is the relationship between two objects and the normal reaction between the object that is in contact with each other.
Free body diagram: It is the representation of the body on a plan that shows all the force acting on the body.

Formula used:
${\text{F = (mg)sin}}\theta {\text{ + }}{\mu _{\text{k}}}({\text{mg)cos}}\theta $, here F is the force acting on the cube body, (mg) is the weight of the cube, \[{\mu _k}\] is the coefficient of friction acting on the cube body.

Complete step-by-step solution:
It is given details, Force acting on the cube, ${\text{mg = 10N}}$, ${\mu _{\text{k}}} = 0.6$, Inclined plane of slope \[3\] in \[5\] means \[3\] in the vertical direction and \[5\] in the horizontal direction. From this we get the values of\[\theta \],$\theta = {\text{si}}{{\text{n}}^{ - 1}}\left( {\dfrac{3}{5}} \right)$

Now, by using the above equation, ${\text{F = (mg)sin}}\theta {\text{ + }}{\mu _{\text{k}}}({\text{mg)cos}}\theta $ and substituting the values we get,
${\text{F = (10)}}\left( {\dfrac{3}{5}} \right){\text{ + 0}}{\text{.6}}(10{\text{)}}\left( {\dfrac{4}{5}} \right){\text{N}}$
$F = 10.8{\text{N}}$

Hence the correct option is (C).

Note:
1. Rough surface has a higher value of coefficient of friction.
2. Temperature can also vary the coefficient of friction.
3. The value of coefficient of friction varies from zero to one.
4. Coefficient of kinetic friction is produced due to the motion between two rough surfaces. 5. The coefficient of kinetic friction depends only on the nature of the surface.
6. Coefficient of static friction is generated due to the two surfaces at rest.
7. The force acting downward due to the gravitational pull is called gravity.
8. The coefficient of friction always acts in opposite to the direction of the motion of the object.