Question

A toy car rolls down the inclined plane as shown in the fig. 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

the answer would be A

Answer 2

When car rolls down the inclined plane from height H, then velocity acquired  by it at the lowest point = v √2g H - (1 eq)

For looping of the loop, velocity at the lowest point should be  = v √5g r - (2 eq)

Thus from equation 1 and 2

v = √2gH = √5gr

Therefore H = 5r/2 --- ( 3 eq)

According to the figure -

H= h+2r

= r = H-h/2

Substituting the value of equation 3 we will get

H = 5/2 [H-h/2]

= H/h = 5

Thus the relationship between H and h is 5