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A block kept on a rough inclined plane , as shown in the figure , remains at rest upto a maximum force 2 N down the inclined plane. The maximum external external force up the inclined plane that does not move the block is 10 N . The coefficient of static friction between the block and the plane is :

[Take g = 10 m/s²]

Option 1)
$\frac{\sqrt{3}}{2}$
Option 2)
$\frac{2}{3}$
Option 3)
$\frac{\sqrt{3}}{4}$
Option 4)
$\frac{1}{2}$

Answers (2)

best_answer

Minimum Force to move a body downward along the surface of Inclined Plane -

Use condition of equilibrium.

$R+P sin \alpha=W cos \lambda$

$F= P cos \alpha + W sin \lambda$

Use $F=\mu R$

$P=\frac{W sin(\theta-\lambda)}{cos(\alpha-\theta)}$

- wherein

P = Pulling force

$\alpha=$ Angle of P with horizontal

$\lambda=$ Inclined angle

R = Reaction

W = Weight

For 2N force

$2+mg \sin \theta = \mu mg\cos 30$ ........(1)

For 10N force

$10= mg\sin 30+\mu mg\cos 30$ ........(2)

From (1) and (2)

$12 = 2\mu mg \cos \left ( 30 \right )$

$8=mg\sin 30$

$\Rightarrow \frac{12}{8} = \mu \cot 30 = 2\mu \times \sqrt{3}$

$\mu =\frac{\sqrt{3}}{2}$

Option 1)
$\frac{\sqrt{3}}{2}$
Option 2)

$\frac{2}{3}$

Option 3)

$\frac{\sqrt{3}}{4}$

Option 4)

$\frac{1}{2}$

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