An object of mass `10 kg` is to be kept at rest on an inclined plane making an angle of `37^(@)`to the horizontal by applying a force `F` along the plane upwards as shown in figure . The coefficient of static fiction between the object and the plane is `0.2` Find the magnitude of force `F`
[Take `g = 10 ms^(-2)]`

Explanation

`mg sin 37^(@) = 10 xx 10 xx 3//5 = 60 N`
`f_(1) = mu N = 0.2 cos37^(@) = 0.2 xx 10 xx 10 xx 4//5 = 16 N`

Friction force alone is balance `mg sin 37^(@)` Hence `F` is required for balancing heretwo cases arise.
Case I : If the block tendency to slide down friction on block will act upward
`F + 16 = 60`
`rArr F = 44N`
This is the maximum force required for balance

Case II : If the block tendency to slide up friction on block will act downward
`F = 60 + 16 rArr F = 76 N`
This is the maximum force required for balancing .
Therefore , for balancing `44 N le F le 76 N`