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To solve this problem, we need to calculate the component of the weight of a body acting perpendicular to an inclined plane.

### Given dataTo solve this problem, we need to calculate the component of the weight of a body acting perpendicular to an inclined plane.

### Given 
- Mass of the body: \( y \, \text{kg} \)
- Angle of the inclined plane with the horizontal: \( \theta = 60^\circ \)

### Key Concept:
The weight of the body \( W \) is given by:
\[
W = y \cdot g
\]
where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \), but in this problem, we're only focusing on the mass for simplicity in the units of kg.wt).

The component of the weight perpendicular to the inclined plane is given by:
\[
W_{\perp} = W \cdot \cos(\theta)
\]
Substituting \( W = y \cdot g \), we have:
\[
W_{\perp} = y \cdot g \cdot \cos(60^\circ)
\]
Since \( \cos(60^\circ) = 0.5 \), this simplifies to:
\[
W_{\perp} = y \cdot g \cdot 0.5 = 0.5 \cdot y \, \text{kg.wt}
\]

### Therefore, the correct answer is (b) \( 0.5 y \).

Would you like a further breakdown of the steps, or have any additional questions?

### Follow-up questions:
1. What is the parallel component of the weight along the plane?
2. How would the result change if the incline angle was \( 30^\circ \)?
3. Why do we use trigonometric functions to calculate weight components on an inclined plane?
4. What is the total force acting on the body in the perpendicular direction if friction is present?
5. How does the smoothness (frictionless nature) of the plane affect the motion of the body?

#### Tip: Always remember that the weight's perpendicular and parallel components depend on the cosine and sine of the angle of inclination respectively.

If you put a body of mass y kg on an inclined smooth plane with 60° to the horizontal, the component of its weight on the direction of perpendicular to the plane is ______ kg.wt.

Solve the problem of finding the weight component perpendicular to an inclined smooth plane with an angle of 60°. This problem involves trigonometry and weight decomposition concepts. Suitable for students in Grades 9-12.

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