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Question #43508

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The Question

Block $A$ of mass $M = 2 \text{ kg}$ rests on a smooth horizontal surface. Block $B$ of mass $m = 1 \text{ kg}$ is placed on top of $A$ . A light inextensible string is attached to $B$ , passes horizontally over a massless, frictionless pulley fixed to the top right edge of $A$ , and is connected to a hanging block $C$ of mass $m_0 = 2 \text{ kg}$ . Block $C$ is in contact with the smooth vertical right face of $A$ . The coefficients of static and kinetic friction between $A$ and $B$ are $\mu_s = 0.5$ and $\mu_k = 0.4$ , respectively. A constant horizontal force $F = 52 \text{ N}$ is applied to block $A$ towards the right. Taking $g = 10 \text{ m/s}^2$ , what is the magnitude of the acceleration of block $B$ relative to the ground?

Options

A.
$12 \text{ m/s}^2$
B.
$17 \text{ m/s}^2$
C.
$16 \text{ m/s}^2$
D.
$10.4 \text{ m/s}^2$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Frame of Reference|Kinetic Friction Transition|Tension in Massless vs Massive Strings

Why This Question Is Tricky

Common Mistakes

This question tests multiple layers of non-inertial mechanics and friction transitions.

The primary trap is forgetting the normal force exerted by the hanging block $C$ on the accelerating base block $A$ ( $N_C = m_0 a_A$ ).

Because $A$ accelerates into $C$ , it must push $C$ horizontally, which creates a reactive force on $A$ that alters the effective inertia of the system.

Omission of this force leads directly to the trap answer of $17 \text{ m/s}^2$ .

Additionally, students may incorrectly assume the tension equals the weight of $C$ ( $T = m_0 g$ ) despite its downward acceleration, or fail to check the static friction boundary, erroneously assuming the system moves as a single unit ( $10.4 \text{ m/s}^2$ ).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Frame of Reference
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free