(C) Given the equations of motion:$x = a \sin(\omega t) \Rightarrow \frac{x}{a} = \sin(\omega t)$$y = a(1 - \cos(\omega t)) \Rightarrow \frac{y}{a} =

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(C) Given the equations of motion:$x = a \sin(\omega t) \Rightarrow \frac{x}{a} = \sin(\omega t)$$y = a(1 - \cos(\omega t)) \Rightarrow \frac{y}{a} = 1 - \cos(\omega t) \Rightarrow \frac{y}{a} - 1 = -\cos(\omega t) \Rightarrow 1 - \frac{y}{a} = \cos(\omega t)$Squaring and adding both equations:$(\frac{x}{a})^2 + (1 - \frac{y}{a})^2 = \sin^2(\omega t) + \cos^2(\omega t)$$\frac{x^2}{a^2} + \frac{(a - y)^2}{a^2} = 1$$x^2 + (y - a)^2 = a^2$This is the equation of a circle with center $(0, a)$ and radius $a$.

Class 11 Physics 3-2.Motion in Plane Mix Examples-Motion in Plane

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$A$ particle moves in the $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$,where $a$ and $\omega$ are constants. The particle traces:

A
a distance proportional to time.
B
a straight line equally inclined to $x$ and $y$ axes.
C
a circle.
D
$(A)$ and $(C)$ both.

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3-2.Motion in Plane

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Mix Examples-Motion in Plane

An aircraft executes a horizontal loop with a speed of $150\, m/s$ with its wings banked at an angle of $12^\circ$. The radius of the loop is .......... $km$ $(g = 10\, m/s^2 \text{ and } \tan 12^\circ = 0.2125)$

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$A$ ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as

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$A$ ball is dropped from a height and falls due to gravity,while wind simultaneously imparts a uniform horizontal acceleration to it. Which one of the following figures best represents its path?

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$A$ body of mass $m$ is projected from the ground with speed $u$ at an angle $\theta$ with the horizontal. The power delivered by gravity to it at half of the maximum height from the ground is

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$A$ car runs at a constant speed on a circular track of radius $100\,m$,taking $62.8\,s$ for every circular lap. The average velocity and average speed for each circular lap respectively are:

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$A$ particle moves in the $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1 - \cos \omega t)$,where $a$ and $\omega$ are constants. The particle traces:

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An aircraft executes a horizontal loop with a speed of $150\, m/s$ with its wings banked at an angle of $12^\circ$. The radius of the loop is .......... $km$ $(g = 10\, m/s^2 \text{ and } \tan 12^\circ = 0.2125)$

$A$ ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as

$A$ ball is dropped from a height and falls due to gravity,while wind simultaneously imparts a uniform horizontal acceleration to it. Which one of the following figures best represents its path?

$A$ body of mass $m$ is projected from the ground with speed $u$ at an angle $\theta$ with the horizontal. The power delivered by gravity to it at half of the maximum height from the ground is

$A$ car runs at a constant speed on a circular track of radius $100\,m$,taking $62.8\,s$ for every circular lap. The average velocity and average speed for each circular lap respectively are:

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