Question

A block of mass 5 kg is placed on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.4. Will the block slide down the plane? If yes, what is the acceleration?

• A. Block will not slide
• B. Block slides with acceleration 0.5 m/s²
• C. Block slides with acceleration 2 m/s²
• D. Block slides with acceleration 9.8 m/s²

Hint:

Compare gravitational force component with maximum friction to check sliding; if sliding, use net force to find acceleration.

Answer 1

The Correct Option is C

Given: Mass, \( m = 5\, \text{kg} \)
Angle of incline, \( \theta = 30^\circ \)
Coefficient of static friction, \( \mu_s = 0.4 \)
Acceleration due to gravity, \( g = 9.8\, \text{m/s}^2 \) Calculate the component of gravitational force down the plane: \[ F_{\text{gravity}} = mg \sin \theta = 5 \times 9.8 \times \sin 30^\circ = 5 \times 9.8 \times 0.5 = 24.5\, \text{N} \] Calculate the maximum static friction force: \[ F_{\text{friction}} = \mu_s N = \mu_s mg \cos \theta = 0.4 \times 5 \times 9.8 \times \cos 30^\circ = 0.4 \times 5 \times 9.8 \times 0.866 = 16.94\, \text{N} \] Since friction force \(16.94\, \text{N}\) is less than the component of gravity \(24.5\, \text{N}\), the block will slide. Net force causing acceleration: \[ F_{\text{net}} = 24.5 - 16.94 = 7.56\, \text{N} \] Acceleration: \[ a = \frac{F_{\text{net}}}{m} = \frac{7.56}{5} = 1.512\, \text{m/s}^2 \] Rounding, acceleration is approximately \(1.5\, \text{m/s}^2\), closest to option (C) 2 m/s².