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Question

A particle is moving with a velocity $$\overline{v} = K (y\hat{i} + x\hat{j})$$, where $$K$$ is a constant. The general equation for its path is:


A
xy=constant
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B
y2=x2+constant
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C
y=x2+constant
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D
y2=x+constant
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Solution

The correct option is B $$y^2 = x^2+constant$$
$$\dfrac{dx}{dt} = ky, \, \dfrac{dy}{dt} = kx$$
Now, $$\dfrac{dy}{dx} = \dfrac{\dfrac{dy}{dt}}{\dfrac{dx}{dt}} = \dfrac{x}{y}$$
$$\Rightarrow ydy = xdx$$
Integrating both side
$$y^2 = x^2 + c$$

Physics

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