Question

A body of 2 kg mass slides down with an acceleration of \( 4 \, \text{ms}^{-2} \) on an inclined plane having a slope of \( 30^\circ \). The external force required to take the same body up the plane with the same acceleration will be (Acceleration due to gravity \( g = 10 \, \text{ms}^{-2} \))

• A. \( 8 \, \text{N} \)
• B. \( 16 \, \text{N} \)
• C. \( 22 \, \text{N} \)
• D. \( 20 \, \text{N} \)

Hint:

While moving up the plane, the external force must overcome both gravity and friction, along with providing the necessary acceleration. Use Newton’s second law along the incline for calculations.

Answer 1

The Correct Option is D

Step 1: Understanding the Given Data
- Mass of the body: \( m = 2 \, \text{kg} \)
- Acceleration while sliding down: \( a = 4 \, \text{ms}^{-2} \)
- Inclination angle: \( \theta = 30^\circ \)
- Acceleration due to gravity: \( g = 10 \, \text{ms}^{-2} \)
Step 2: Finding the Net Force while Sliding Down
The equation of motion along the incline while sliding down is: \[ mg \sin\theta - F_{\text{friction}} = ma \] \[ (2 \times 10) \sin 30^\circ - F_{\text{friction}} = 2 \times 4 \] \[ 10 - F_{\text{friction}} = 8 \] \[ F_{\text{friction}} = 2 \, \text{N} \] Step 3: Finding the Required Force to Move Up
For moving up with the same acceleration: \[ F_{\text{external}} - mg \sin\theta - F_{\text{friction}} = ma \] \[ F_{\text{external}} - 10 - 2 = 8 \] \[ F_{\text{external}} = 20 \, \text{N} \] Step 4: Conclusion
Thus, the external force required to take the body up with the same acceleration is: \[ \mathbf{20 \, \text{N}}. \]