A particle moves such that its position coordinates (x, y) are given by x = 2t and y = t^2. The equation of its trajectory is: MCQ with Answer and Explanation

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A particle moves such that its position coordinates (x, y) are given by x = 2t and y = t^2. The equation of its trajectory is:

A. y = 2x^2

B. y = x^2 / 4

C. y = x

D. y = x^2 / 2

Answer: Option B

Solution (By JKExamLibrary)

The equation of trajectory represents the path of the particle in the x-y plane, eliminating the time variable 't'. Given x = 2t, we can write t = x/2. Substitute this into the y equation: y = t^2 = (x/2)^2 = x^2 / 4. This confirms the particle moves in a parabolic path.

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C. 1Ω

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Explanation:
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The electric field due to an infinite plane sheet of charge with surface charge density σ is:

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Correct Answer: Option D

Explanation:
Using Gauss's law, for an infinite sheet, electric field E = σ/(2ε₀), directed perpendicular to the sheet. This is uniform and independent of distance from the sheet. Option A is for field near conductor surface; C and D are incorrect. Memory aid: 'Infinite sheet: E = σ/(2ε₀); conductor surface: E = σ/ε₀'. This conceptual question tests electrostatics fundamentals, crucial for competitive exams. Always distinguish between conducting and non-conacting sheets, as field expressions differ due to charge distribution.

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