Question

A toy car rolls down the inclined plane as shown in the above figure. It loops at the bottom. What is the relation between $H$ and $h$?

• A. $\frac{H}{h}=2$
• B. $\frac{H}{h}=3$
• C. $\frac{H}{h}=4$
• D. $\frac{H}{h}=5$

Answer 1

Answer: (D)

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

$v^2=u^2+2gH$

where, $u=0$

$v=\sqrt{2}gH.......\left(1\right)$

Velocity at the lowest point should be $v=\sqrt{5}gr...........\left(2\right)$

Thus from equation 1 and 2

$v=\sqrt{2}gH=\sqrt{5}gr$

therefore $H=\frac{5r}{2}..........\left(3\right)$

from figure-

$H=h+2r$

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

substituting the value of equation 3 we will get

$H=\frac{5}{2}[H-\frac{h}{2}]$

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