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Question #43506

Difficulty: 8/10 | 🟢 Free

The Question

A long trolley moves along a straight horizontal track with a velocity that varies with time as $v_T = \alpha t^2$ , where $\alpha = 2 \text{ m/s}^3$ and $t$ is the time in seconds. A block of mass $2 \text{ kg}$ is placed on the smooth horizontal floor of the trolley. At $t = 0$ , the block is at rest relative to the trolley, and a constant horizontal force of $10 \text{ N}$ is applied to the block in the direction of the trolley's motion. What is the work done by the pseudo force on the block, as observed in the reference frame of the trolley, during the time interval $t = 0$ to $t = 2 \text{ s}$ ?

Options

A.
$-\frac{128}{3} \text{ J}$
B.
$-\frac{224}{3} \text{ J}$
C.
$-\frac{112}{3} \text{ J}$
D.
$4 \text{ J}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Frame of Reference|Non-Uniform Acceleration Constraint|Work, Energy, and Power

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Work-Energy Theorem in a non-inertial frame with variable acceleration.

Students often incorrectly assume the pseudo force is constant or calculate its work as $W = -m a_{avg} \Delta x_{rel}$ , leading to incorrect trap options.

Because the trolley's acceleration $a_T(t)$ is time-dependent, the pseudo force is non-conservative and its work must be rigorously evaluated via the integral $\int (-m a_T) \cdot dx_{rel}$ .

Alternatively, students must correctly apply the modified Work-Energy Theorem ( $W_{ext} + W_{pseudo} = \Delta K_{rel}$ ) to bypass the complex integration, which requires a deep conceptual understanding of energy transformations across reference frames.

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