Question

If the maximum acceleration of a moving platform to keep a box of mass \(5\) kg on it without sliding is \(3\ \text{m s}^{-2}\), then the static friction between the box and floor of the platform is (\(g = 10\ \text{m s}^{-2}\))

• A. $0.15$
• B. $0.25$
• C. $0.30$
• D. $0.35$
• E. $0.4$

Hint:

For no slipping condition: - $\mu_s = \frac{a}{g}$ - Mass cancels out, so value is independent of mass

Answer 1

The Correct Option is C

Concept: For a body on an accelerating surface without slipping: \[ f_{\text{max}} = \mu_s N \] Also, friction provides the necessary acceleration: \[ ma = f_{\text{max}} \]

Step 1: Write the force equation.
\[ ma = \mu_s mg \]

Step 2: Cancel mass $m$.
\[ a = \mu_s g \]

Step 3: Solve for $\mu_s$.
\[ \mu_s = \frac{a}{g} = \frac{3}{10} = 0.3 \]