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Question #42399
The Question
An elevator accelerates vertically upwards with a constant acceleration . Inside the elevator, a fixed vertical circular track of radius is completely submerged in a stationary, incompressible ideal fluid of density . A small spherical shell of negligible mass and volume , completely filled with another incompressible fluid of density , is projected tangentially from the lowest point of the track's interior. Assuming no viscous drag, what is the minimum initial speed relative to the track required for the sphere to just complete the vertical loop?
Options
- A.
- B.
- C.
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Multi-Concept_Bridge
Master problems that require linking physics and math concepts to solve complex competitive questions.
Concepts Behind This Question
Minimum Speed for Looping|Apparent Weight in Accelerating Elevators|Accelerated Frame Hydrostatics|Vector Analysis
Why This Question Is Tricky
Common Mistakes
This question tests the student's ability to correctly apply non-inertial frame transformations to both solid mechanics and hydrostatics.
A common trap is assuming buoyancy remains even in an accelerating frame, failing to realize that the hydrostatic pressure gradient scales with .
Another mistake is forgetting to divide the net effective weight by the actual mass () to find the modified kinematic acceleration .
By combining the looping condition with an accelerating fluid, it forces a rigorous re-derivation of the critical velocity rather than relying on rote memorization of .
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Motion in a Plane - Class 11 Part 1 |
| Concept | Minimum Speed for Looping |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |