A mass of `2 kg` lies on a plane making an anged `30^(0)` to the horizontal. Resolve its weight along and perpendicular to the plane. Assume `g=10 ms^(-2)`.

Explanation

To resolve the weight of a mass of 2 kg lying on a plane inclined at an angle of 30 degrees to the horizontal, we will follow these steps:

### Step 1: Calculate the weight of the mass
The weight (W) of the mass can be calculated using the formula:
\[ W = mg \]
where:
- \( m = 2 \, \text{kg} \) (mass)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ W = 2 \, \text{kg} \times 10 \, \text{m/s}^2 = 20 \, \text{N} \]

### Step 2: Identify the angle of inclination
The angle of inclination (θ) is given as:
\[ θ = 30^\circ \]

### Step 3: Resolve the weight into components
To resolve the weight into components along and perpendicular to the inclined plane, we use trigonometric functions.

#### Component perpendicular to the plane (N):
The component of the weight acting perpendicular to the inclined plane is given by:
\[ N = W \cos(θ) \]
Substituting the values:
\[ N = 20 \, \text{N} \cos(30^\circ) \]

Using the value of \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \):
\[ N = 20 \, \text{N} \times \frac{\sqrt{3}}{2} = 10\sqrt{3} \, \text{N} \]

#### Component along the plane (F):
The component of the weight acting along the inclined plane is given by:
\[ F = W \sin(θ) \]
Substituting the values:
\[ F = 20 \, \text{N} \sin(30^\circ) \]

Using the value of \( \sin(30^\circ) = \frac{1}{2} \):
\[ F = 20 \, \text{N} \times \frac{1}{2} = 10 \, \text{N} \]

### Final Results
- The component of weight perpendicular to the plane: \( N = 10\sqrt{3} \, \text{N} \)
- The component of weight along the plane: \( F = 10 \, \text{N} \)