Question

As shown in figure, a $70 kg$ garden roller is pushed with a force of $\vec{F}=200 N$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g=10 m s ^{-2}$ )

• A. $800 N$
• B. $600 N$
• C. $200 \sqrt{3} N$
• D. $800 \sqrt{2} N$

Hint:

The normal reaction is the force exerted by a surface perpendicular to the object. In problems involving inclined planes or angles, use the component of the applied force in the direction of the normal to calculate the total normal reaction.

Answer 1

The Correct Option is A

To find the normal reaction on the garden roller, we need to analyze the forces acting on it. The roller has a weight, a horizontal force, and a normal reaction.

Step-by-step Solution:
 

The normal reaction \( N \) is given by the formula:

\[ N = mg + F \sin 30^\circ \]

where:

• \( m = 70 \, \text{kg} \),
• \( g = 10 \, \text{m/s}^2 \),
• \( F = 200 \, \text{N} \).

Now,

\[ N = 700 + 200 \times \sin 30^\circ = 700 + 200 \times \frac{1}{2} = 700 + 100 = 800 \, \text{N} \]

Thus, the normal reaction is 800 N.