A particle is moving with velocity v =K(y i +x j ) , where K is a constant. The general equation for its path is

Correct answer: D. y^2=x^2+ constant v =K y i +K x j (d x)/(d t)=K y, (d y)/(d t)=K x (d y)/(d x)=(d y)/(d t) × (d t)/(d x)=(K x)/(K y) y d y=x d x y^2=x^2+c

JEE Main 2010

Exam: JEE Main
Year: 2010
Subject: Physics
Chapter: Motion in Two Dimensions

JEE Main 2010 · Physics · Motion in Two Dimensions

A particle is moving with velocity v =K(y i +x j ) , where K is a...

A particle is moving with velocity

\overrightarrow{\mathrm{v}}=\mathrm{K}(\mathrm{y} \hat{\mathrm{i}}+\mathrm{x} \hat{\mathrm{j}})

, where

\mathrm{K}

is a constant. The general equation for its path is

Options

A $y=x^2+$ constant
B $y^2=x+$ constant
C $x y=$ constant
D $y^2=x^2+$ constant

Correct answer

D. $y^2=x^2+$ constant

Step-by-step solution

\vec{v}=K y \hat{i}+K x \hat{j}

\frac{d x}{d t}=K y, \quad \frac{d y}{d t}=K x

\frac{d y}{d x}=\frac{d y}{d t} \times \frac{d t}{d x}=\frac{K x}{K y}

y d y=x d x

y^2=x^2+c

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