A toy car rolls down the inclined plane as shown in the fig.... | PHYSICS - UNIFORM CIRCULAR MOTION | SolveeIt

A toy car rolls down the inclined plane as shown in the fig. It goes around the loop at the bottom. What is the relation between $H$ and $h$

$\frac{H}{h} = 2$

$\frac{H}{h} = 3$

$\frac{H}{h} = 4$

$\frac{H}{h} = 5$

Answer

$\frac{H}{h} = 5$

Explanation

When car rolls down the inclined plane from height H, then velocity acquired by it at the lowest point

$v = \sqrt{2gH}$ ….(i)

and for looping of loop, velocity at the lowest point should be $v = \sqrt{5gr}$ ….(ii)

From eqⁿ (i) and (ii) $v = \sqrt{2gH} = \sqrt{5gr}$ ∴ $H = \frac{5r}{2}$ .(iii)

From the figure $H = h + 2r$ ⇒ $r = \frac{H - h}{2}$

Substituting the value of r in equation (iii) we get $H = \frac{5}{2}\left\lbrack \frac{H - h}{2} \right\rbrack$ ⇒ $\frac{H}{h} = 5$

Question: A toy car rolls down the inclined plane as shown in the fig. It goes around the loop at the bottom. ...