A smooth circular groove has a smooth vertica | vedclass

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(A) For a block of mass $m$ moving in a circular path of radius $r$ with speed $v$,the centripetal force required is provided by the normal reaction $

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(A) For a block of mass $m$ moving in a circular path of radius $r$ with speed $v$,the centripetal force required is provided by the normal reaction $(N)$ exerted by the vertical wall.The centripetal force is given by the formula:$F_c = \frac{m v^2}{r}$Since the normal reaction $(N)$ provides this centripetal force,we have:$N = \frac{m v^2}{r}$Here,$m$ and $r$ are constants. Therefore,the relationship between $N$ and $v$ is:$N \propto v^2$This equation represents a parabola of the form $Y = kX^2$,where $Y = N$,$X = v$,and $k = \frac{m}{r}$.Thus,the graph of $N$ versus $v$ is a parabola opening upwards,which corresponds to the curve shown in option $A$.

$A$ smooth circular groove has a smooth vertical wall as shown in the figure. $A$ block of mass $m$ moves against the wall with a speed $v$. Which of the following curves represents the correct relation between the normal reaction $(N)$ on the block by the wall and the speed of the block $(v)$?

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