Question

A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12. Keeping the box in stationary state over the trolley, the maximum acceleration with which the trolley can be moved horizontally in m s⁻² is: ____.

• A. 1.2
• B. 1.8
• C. 1.5
• D. 2.1

Hint:

Notice that the mass of the box (15 kg) is irrelevant to the final answer. In friction-limited acceleration problems, the mass always cancels out!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When the trolley accelerates, the box experiences a pseudo force in the opposite direction. For the box to remain stationary relative to the trolley, the static frictional force must balance this pseudo force.

Step 2: Key Formula or Approach:
1. Pseudo force ($F_p$) = $ma$ 2. Maximum static friction ($f_s$) = $\mu_s N = \mu_s mg$ 3. For no slipping: $ma \leq \mu_s mg$

Step 3: Detailed Explanation:
1. The maximum possible acceleration ($a_{max}$) occurs when the pseudo force is exactly equal to the limiting friction. 2. Cancel 'm' from both sides: \[ a_{max} = \mu_s g \] 3. Substitute the given values ($\mu_s = 0.12$ and taking $g = 10 \text{ m/s}^2$ for standard calculation): \[ a_{max} = 0.12 \times 10 = 1.2 \text{ m/s}^2 \]

Step 4: Final Answer:
The maximum acceleration is 1.2 m/s².