A body initially at rest and sliding along a frictionless track from a height ' $h$ ' (as shown in figure) just completes a vertical circle of diameter $A B = d$ . The height ' $h$ ' is equal to

Question

A body initially at rest and sliding along a frictionless track from a height ' h ' (as shown in figure) just completes a vertical circle of diameter A B = d . The height ' h ' is equal to

TestHub · Accepted Answer

For a body to just complete a vertical circle of radius $R$ , the minimum velocity required at the lowest point is $v = 5 g R$ .

Given the diameter of the circle is $d$ , the radius is $R = \frac{d}{2}$ .

Therefore, the velocity at the lowest point must be:
$v = \frac{5 g d}{2}$

By the principle of conservation of mechanical energy, the potential energy of the body at height $h$ is converted into kinetic energy at the lowest point (assuming the lowest point is the reference level for zero potential energy).

$m g h = \frac{1}{2} m v^{2}$

Substituting the value of $v^{2}$ :
$m g h = \frac{1}{2} m (\frac{5 g d}{2})$

$h = \frac{5 d}{4}$

Answer: $\frac{5}{4} d$

Physics - W.E.P. Question with Solution | TestHub

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