Question

A body of mass \( 5 \, \text{kg} \) is placed on a frictionless inclined plane of angle \( 30^\circ \). What is the component of the weight of the body along the plane?

• A. \( 25 \, \text{N} \)
• B. \( 50 \, \text{N} \)
• C. \( 45 \, \text{N} \)
• D. \( 75 \, \text{N} \)

Hint:

Remember: The component of the weight along the plane depends on both the mass of the body and the angle of inclination. For an inclined plane, \( \sin \theta \) gives the projection of the weight along the surface.

Answer 1

The Correct Option is A

Step 1: Apply the formula for the weight component on an inclined plane The formula for the component of weight parallel to an inclined plane is: \[ W_{\parallel} = mg \sin \theta \] Here: - \( m \) represents the mass of the object. - \( g \) denotes the acceleration due to gravity. - \( \theta \) signifies the angle of inclination. Step 2: Input the provided values Given: - Mass \( m = 5 \, \text{kg} \) - Gravitational acceleration \( g = 10 \, \text{m/s}^2 \) - Inclination angle \( \theta = 30^\circ \) Substitute these values into the formula: \[ W_{\parallel} = 5 \times 10 \times \sin(30^\circ) = 50 \times \frac{1}{2} = 25 \, \text{N} \] Answer: The component of the body's weight along the plane is \( 25 \, \text{N} \). The correct option is (1).