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(C) The velocity $v_1$ is given by the derivative of $y_1$ with respect to time $t$: $v_1 = \frac{dy_1}{dt} = 0.1 	imes 100\pi \cos(100\pi t + \frac{

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$\frac{-\pi}{6}$

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(C) The velocity $v_1$ is given by the derivative of $y_1$ with respect to time $t$: $v_1 = \frac{dy_1}{dt} = 0.1 	imes 100\pi \cos(100\pi t + \frac{\pi}{3}) = 10\pi \cos(100\pi t + \frac{\pi}{3})$.The velocity $v_2$ is given by the derivative of $y_2$ with respect to time $t$: $v_2 = \frac{dy_2}{dt} = 0.1 	imes (-100\pi) \sin(100\pi t) = -10\pi \sin(100\pi t)$.To compare the phase,we express $v_2$ as a cosine function: $v_2 = 10\pi \cos(100\pi t + \frac{\pi}{2})$.The phase of $v_1$ is $\phi_1 = 100\pi t + \frac{\pi}{3}$ and the phase of $v_2$ is $\phi_2 = 100\pi t + \frac{\pi}{2}$.The phase difference $\Delta\phi = \phi_1 - \phi_2 = (100\pi t + \frac{\pi}{3}) - (100\pi t + \frac{\pi}{2}) = \frac{\pi}{3} - \frac{\pi}{2} = -\frac{\pi}{6}$.

Column-$I$	Column-$II$
$A$. Tapetum	$i$. Degenerate during development
$B$. Intine	$ii$. Resistant organic materials
$C$. Vegetative cell	$iii$. Pollen tube
$D$. Sporopollenin	$iv$. Provide nourishment to pollen grains

Two simple harmonic motions are represented by the equations $y_1 = 0.1 \sin(100\pi t + \frac{\pi}{3})$ and $y_2 = 0.1 \cos(100\pi t)$. The phase difference of the velocity of particle $1$ with respect to the velocity of particle $2$ is

Similar Questions

Match the items in Column-$I$ with those in Column-$II$:

Column-$I$ Column-$II$

$A$. Tapetum $i$. Degenerate during development

$B$. Intine $ii$. Resistant organic materials

$C$. Vegetative cell $iii$. Pollen tube

$D$. Sporopollenin $iv$. Provide nourishment to pollen grains

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