Question

A body of mass 5 kg is placed on a frictionless inclined plane of angle 30°. What is the component of the weight of the body along the plane?

• A. 25 N
• B. 50 N
• C. 45 N
• D. 75 N

Hint:

Remember: The component of the weight along an inclined plane is found using \( W_{\parallel} = W \sin(\theta) \), where \( \theta \) is the angle of the incline.

Answer 1

The Correct Option is A

Given: Mass \( m = 5 \, \text{kg} \)
Gravitational acceleration \( g = 10 \, \text{m/s}^2 \)
Angle of incline \( \theta = 30^\circ \)

Step 1: Calculate the weight
Weight \( W \) is calculated as \( W = mg \).
Substituting the given values: \( W = (5 \, \text{kg})(10 \, \text{m/s}^2) = 50 \, \text{N} \)

Step 2: Calculate the component of weight along the plane
The component of weight along the plane, \( W_{\parallel} \), is given by \( W_{\parallel} = W \sin(\theta) \).
Substituting the values: \( W_{\parallel} = 50 \, \text{N} \times \sin(30^\circ) = 50 \, \text{N} \times \frac{1}{2} = 25 \, \text{N} \)

Step 3: Conclusion
The component of the body's weight along the plane is \( 25 \, \text{N} \).

Answer: The correct answer is option (1): 25 N.