Question

A body of mass \(2 \, {kg}\) is placed on a smooth horizontal surface. Two forces \(F_1 = 20 \, {N}\) and \(F_2 = 10\sqrt{3} \, {N}\) are acting on the body in the directions making angles of \(30^\circ\) and \(60^\circ\) to the surface. The reaction of the surface on the body is: 

 

• A. \(20 \, {N}\)
• B. \(25 \, {N}\)
• C. \(5 \, {N}\)
• D. Zero

Hint:

In problems involving forces on horizontal surfaces, always check for the vertical components of all forces to determine the correct normal reaction.

Answer 1

The Correct Option is D

The forces \( F_1 \) and \( F_2 \) are acting at angles to the horizontal surface. We need to find the reaction force exerted by the surface.

The horizontal components of the forces \( F_1 \) and \( F_2 \) do not affect the vertical reaction of the surface because they do not contribute to the vertical force.

The vertical components of the forces \( F_1 \) and \( F_2 \) are responsible for the reaction from the surface. The vertical component of each force is given by:

\[ F_{1v} = F_1 \sin 30^\circ = 20 \times \frac{1}{2} = 10 \, \text{N} \] \[ F_{2v} = F_2 \sin 60^\circ = 10\sqrt{3} \times \frac{\sqrt{3}}{2} = 15 \, \text{N} \]

The total vertical force acting on the body is the sum of the vertical components of the forces \( F_1 \) and \( F_2 \):

\[ F_{\text{total vertical}} = 10 + 15 = 25 \, \text{N} \]

The body is in equilibrium, so the reaction force from the surface must balance the total vertical force, which would typically be \( 25 \, \text{N} \) downward.

However, because the surface is smooth and the body is not moving vertically, the net reaction from the surface in the vertical direction is zero due to the exact cancellation of forces acting on the body.

Thus, the reaction force is zero.