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 of the body, \( m = 5 \, \text{kg} \) 
Gravitational acceleration, \( g = 10 \, \text{m/s}^2 \) 
Angle of the plane, \( \theta = 30^\circ \) 

Step 1: Weight of the body The weight \( W \) of the body is given by: \[ W = mg \] Substitute the given values: \[ W = (5 \, \text{kg})(10 \, \text{m/s}^2) = 50 \, \text{N} \] 

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

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

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