JEE Main 2023PhysicsRay OpticsEasyNumerical

JEE Main 2023 — Ray Optics Question with Solution

JEE Main 2023 (13 Apr Shift 1)

Question

A fish rising vertically upward with a uniform velocity of 8 m s–1, observes that a bird is diving vertically downward towards the fish with the velocity of 12 m s–1. If the refractive index of water is 43, then the actual velocity of the diving bird to pick the fish, will be__________m s-1.

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Show full solutionCorrect answer: 3
Correct answer
3

Step-by-step explanation

Let the fish be at a depth x from the surface and let the bird be at height y from the surface. So, with respect to fish

y'=μy+x⇒y'=4y3+x

Differentiating with respect to time,

dy'dt=4dy3dt+dxdt

⇒4y3+dxdt=-12

⇒43·dydt=-12+8=-4

⇒dydt=-3 m s-1

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About this question

This is a previous-year question from JEE Main 2023, covering the Ray Optics chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.