Question

A plane flies a loop circle at uniform speed $u$. The pilot experiences an apparent weight at the bottom which is double his apparent weight at the top of the circular path. The acceleration due to gravity is $g$. If the radius of the path is $\frac{n{u}^2}{g}$, find $n$.

• A. $3$
• B. $6$
• C. $5$
• D. $8$

Answer 1

The correct option is A $3$

At the top of the circular path
$W-N=F_c$
Pilot's apparent weight at top (t) $=N_t=mg-\frac{m{u}^2}{r}$
At bottom : $N-W=F_c$
Pilot's apparent weight at bottom (b)$=N_b=mg+\frac{m{u}^2}{r}$
By data : $N_b=2N_t$
$\Rightarrow mg+\frac{m{u}^2}{r}=2[mg-\frac{m{u}^2}{r}]$
$\Rightarrow mg=\frac{3m{u}^2}{r}$
$\Rightarrow r=\frac{3u^2}{g}$
$\Rightarrow n=3$