A block of mass √(3) kg resting on a horizontal surface. A...

A block of mass $\sqrt{3} \mathrm{~kg}$ resting on a horizontal surface. A force $F$ is applied on the block as shown in figure. If coefficient of friction between the block be $\frac{1}{2 \sqrt{3}}$ what can be the maximum value of force $F$ so that block does not start moving? (Take $g=10 \mathrm{~ms}^{-2}$ ) (a) $20 \mathrm{~N}$ (b) $10 \mathrm{~N}$ (c) $12 \mathrm{~N}$ (d) $15 \mathrm{~N}$

A block of mass $\sqrt{3} \mathrm{~kg}$ resting on a horizontal surface. A force $F$ is applied on the block as shown in figure. If coefficient of friction between the block be $\frac{1}{2 \sqrt{3}}$ what can be the maximum value of force $F$ so that block does not start moving? (Take $g=10 \mathrm{~ms}^{-2}$ )
(a) $20 \mathrm{~N}$
(b) $10 \mathrm{~N}$
(c) $12 \mathrm{~N}$
(d) $15 \mathrm{~N}$

Key Concepts

Force Resolution

Force resolution involves breaking down a force into its horizontal and vertical components. This process is crucial when dealing with forces applied at an angle, as it allows for the independent analysis of forces that affect both the normal force and the tendency of the object to move horizontally.

Equilibrium Conditions

Equilibrium conditions refer to the state in which an object remains at rest because the sum of all forces acting upon it is zero. For problems involving friction, ensuring equilibrium means that the applied force must not exceed the maximum static frictional force, thereby preventing motion.

Static Friction

Static friction is the resistive force that prevents an object from starting to move when an external force is applied. It has a maximum value that is determined by the product of the coefficient of static friction and the normal force. Understanding static friction is vital in determining the threshold at which an object transitions from rest to motion.

Normal Force

The normal force is the reactive force exerted by a surface to support the weight of an object resting on it, acting perpendicular to the surface. It is essential in friction problems because the frictional force is directly proportional to the normal force; any additional vertical components of applied forces can change the magnitude of this force.

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