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(D) The speed $v$ at which the tape moves towards the reel is given by the relation $v = \omega R$,where $\omega$ is the angular velocity of the reel

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(D) The speed $v$ at which the tape moves towards the reel is given by the relation $v = \omega R$,where $\omega$ is the angular velocity of the reel and $R$ is its current radius.Given that the reel rotates with a constant angular velocity,$\omega = 	ext{constant}$.The radius $R$ of the reel is increasing at a steady rate,which means $\frac{dR}{dt} = 	ext{constant}$.To find the variation of speed $v$ with time $t$,we differentiate the expression for $v$ with respect to time:$\frac{dv}{dt} = \frac{d}{dt}(\omega R) = \omega \cdot \frac{dR}{dt}$.Since both $\omega$ and $\frac{dR}{dt}$ are constants,their product $\frac{dv}{dt}$ is also a constant.$A$ constant rate of change of speed with respect to time implies that the $v-t$ graph is a straight line with a constant positive slope.

Column $I$	Column $II$
$(A)$ $u_x$ is doubled, $u_y$ is halved	$(p)$ $H$ will remain unchanged
$(B)$ $u_y$ is doubled, $u_x$ is halved	$(q)$ $R$ will remain unchanged
$(C)$ $u_x$ and $u_y$ both are doubled	$(r)$ $R$ will become four times
$(D)$ Only $u_y$ is doubled	$(s)$ $H$ will become four times

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