PYQ + trends

1. TITLE

NEET 2023 Q7: Trend: Why the "Max Acceleration" of a truck depends only on $\mu_s$ — Full solution + Why they asked this

2. THE ACTUAL NEET QUESTION

NEET 2023 — Question
Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 ($g=10\text{ m s}^{-2}$).
A) $150\text{ m s}^{-2}$
B) $1.5\text{ m s}^{-2}$
C) $50\text{ m s}^{-2}$
D) $1.2\text{ m s}^{-2}$

3. OFFICIAL ANSWER

NEET Answer Key: (B)

4. COMPLETE SOLUTION

Step-by-step calculation:
1. Let the mass of the body lying on the floor be $m$.
2. When the car accelerates forward with acceleration $a$, the body experiences a pseudo force $ma$ in the backward direction (relative to the car).
3. The only force opposing this impending backward motion is the static friction ($f_s$) between the body and the floor, acting in the forward direction.
4. For the body to remain stationary relative to the car, the static friction must balance the pseudo force:
$ma = f_s$
5. The maximum value of static friction (limiting friction) is given by:
$f_{s(max)} = \mu_s N = \mu_s mg$
6. Therefore, for maximum acceleration ($a_{max}$):
$m a_{max} = \mu_s mg$
7. Notice that the mass ($m$) cancels out on both sides:
$a_{max} = \mu_s g$
8. Substitute the given values ($\mu_s = 0.15$, $g = 10\text{ m s}^{-2}$):
$a_{max} = 0.15 \times 10 = 1.5\text{ m s}^{-2}$

Formula used:
$a_{max} = \mu_s g$

Why this approach:
Static friction is a self-adjusting force. It provides the necessary acceleration to the box to keep it stationary relative to the accelerating platform. By equating the pseudo force to the limiting static friction, we find the critical threshold before slipping occurs.

5. WHY NEET ASKED THIS

Explain the examiner's intent:
- What concept were they testing? The examiner wanted to test if students understand that static friction is what accelerates an object placed on a moving platform, and that this maximum acceleration is completely independent of the object's mass.
- What's the common mistake they expected students to make? Students often get confused when the mass of the body or the car is not provided, thinking the problem has missing data.
- Which option was the "trap"? Option (A) $150\text{ m s}^{-2}$ and Option (C) $50\text{ m s}^{-2}$ were traps for students who might incorrectly multiply/divide by $g$ multiple times or misplace the decimal point during calculation.

6. TREND ANALYSIS

Year How they asked Twist
2023 Block on the horizontal floor of an accelerating car. Direct application of $a_{max} = \mu_s g$. Mass was not given, testing formula independence.
2010 Block in contact with the vertical inner wall of an accelerating cart The normal force (N) is provided by the pseudo force (mα), and friction acts vertically to balance weight (mg). The condition flips to $\alpha \ge g/\mu$.
2001 Block on an accelerating truck, asking for the actual frictional force.  The truck's acceleration ($5\text{ m s}^{-2}$) was less than the maximum possible ($6\text{ m s}^{-2}$). Students had to realize friction is self-adjusting and equal to ma=5 N, not limiting friction ($\mu_s mg = 6\text{ N}$).

Prediction for NEET 2026:
Expect a variation testing the self-adjusting nature of static friction (like 2001) or a combination scenario where a block is on an inclined plane inside an accelerating vehicle (pseudo force + inclined plane components).

7. SIMILAR QUESTIONS TO PRACTICE

"If you understood this, you can solve:"
- NEET 2010 Q37: Acceleration of a cart to prevent a block from falling down its vertical face.Mock exams
- NEET 2001 Q52: Finding exact frictional force when truck acceleration is less than $\mu_s g$.
- NEET 2012 Q32: Maximum speed of a car on a level circular track without slipping ($v_{max} = \sqrt{\mu_s Rg}$).

8. QUICK REVISION FOR THIS TYPE

For "Accelerating Platform + Friction" questions, always:

  • First check: Is the block on a horizontal floor or pressed against a vertical wall? (This changes your Normal Force from $mg$ to $ma$).
  • Then apply: Newton's second law using pseudo force ($F_{pseudo} = ma$). Equate it to friction.
  • Watch out for: The exact value of acceleration given! If the applied pseudo force ($ma$) is LESS than the limiting friction ($\mu_s mg$), the actual friction acting is just $ma$, not $\mu_s mg$.

9. NCERT BASE

This question tests: NCERT Class 11 Physics, Chapter 4 (Laws of Motion).
Fun fact: This exact question is a direct copy of NCERT Example 4.7 (Determine the maximum acceleration of the train in which a box lying on its floor will remain stationary...).

10. CTA

All PYQs from this chapter → Laws of Motion Guide
Practice similar questions → Mock exams