Question

A block is lying at rest inside a bus. The maximum acceleration of the bus such that the block remain stationary is \((\text{the static friction coefficient}=0.2,\ \text{acceleration due to gravity}=10\,\text{m s}^{-2})\)

• A. \(1\,\text{m s}^{-2}\)
• B. \(0.5\,\text{m s}^{-2}\)
• C. \(2\,\text{cm s}^{-2}\)
• D. \(2\,\text{m s}^{-2}\)

Hint:

For a block to remain at rest on an accelerating horizontal surface, static friction must satisfy \[ ma\leq \mu_s mg. \] Hence the maximum acceleration is \[ a_{\max}=\mu_s g. \]

Answer 1

The Correct Option is D

Step 1: Identify forces on the block.
Only static friction provides horizontal force: f_s = ma. Maximum static friction = μ_s N = μ_s mg.

Step 2: Set no-slip condition.
ma ≤ μ_s mg → a ≤ μ_s g.

Step 3: Plug in numbers.
a_max = 0.2 × 10 = 2 m/s².

Step 4: Final Answer:
2 m/s².