Question

A pilot of mass m can withstand a maxirnum apparent weight 6 times ofmg. The minimum radius o curvature o circle in which the aeroplane dives up from the lowest point with a speed 504kmph is

• A. 200 m
• B. 300 m
• C. 400 m
• D. 500m

Answer 1

The correct option is C 400 m

$\begin{array}{c}\text{Given-}\pi \text{Pilot can withstand apparent weight of}6mg\\ \ast \text{speed at lowest point}=504kmph=140mls\\ \text{Fora at lowest point is given by -}\end{array}$

$\begin{array}{c}F=mg+\frac{m{v}^2}{R}-(1R=\text{Raclius of curverture}\\ \Rightarrow \text{From the given conditions -}\\ F⩽6mg\\ \Rightarrow \text{we get}\\ mg+\frac{m{v}^2}{R}⩽6mg\\ \Rightarrow \frac{v^2}{R}⩽5g\\ \Rightarrow \text{we get}R⩾\frac{v^2}{5g}\end{array}$

$\begin{array}{cc}R& ⩾\frac{(140{)}^2}{5\times 10}\\ \Rightarrow R⩾392m& \Rightarrow R\approx 400m\\ \text{Hence, the minimum Radius is}400m& \end{array}$