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Question #43504

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m = 2 \text{ kg}$ moves on a smooth horizontal plane. Its position in polar coordinates $(r, \theta)$ is given by $r(t) = 2 + \sin(\pi t)$ meters and $\theta(t) = 2t$ radians, where $t$ is the time in seconds. The particle is subjected to a net force $\vec{F}$ which can be resolved into a radial component $F_r$ and a tangential component $F_t$ . Let $W_t$ be the work done by the tangential force $F_t$ and $W_{\text{net}}$ be the work done by the net force $\vec{F}$ on the particle during the time interval $t = 0$ to $t = 0.5 \text{ s}$ . Which of the following gives the correct values of $(W_t, W_{\text{net}})$ ?

Options

A.
$(20 - \pi^2 \text{ J}, 20 - \pi^2 \text{ J})$
B.
$(40 \text{ J}, 20 - \pi^2 \text{ J})$
C.
$(40 \text{ J}, 40 \text{ J})$
D.
$(20 + \pi^2 \text{ J}, 40 \text{ J})$

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

Power-Velocity Relationship|Non-Uniform Circular Motion|Principle of Homogeneity Exceptions

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between the work done by a tangential force and the net work done on a particle in a system with a varying radius.

A common misconception is assuming that the radial (centripetal) force never does work, leading students to incorrectly equate the net work (change in kinetic energy) entirely to the work done by the tangential force ( $W_t = \Delta K$ ).

By introducing a time-dependent radius, the radial velocity $\dot{r}$ becomes non-zero, meaning the radial force $F_r$ does work ( $W_r = \int F_r dr$ ).

Students who fall for the trap will calculate $\Delta K$ and incorrectly select the option where $W_t = W_{\text{net}} = 20 - \pi^2 \text{ J}$ , failing to integrate the tangential power $P_t = F_t v_t$ independently.

Quick Facts About This Question

Question Information

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