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3-2.Motion in Plane
hard
A particle is projected from ground at an angle $\theta$ with horizontal with speed $u$. The ratio of radius of curvature of its trajectory at point of projection to radius of curvature at maximum height is ........
A
$\frac{1}{\sin ^2 \theta \cos \theta}$
B
$\cos ^2 \theta$
C
$\frac{1}{\sin ^3 \theta}$
D
$\frac{1}{\cos ^3 \theta}$
Solution

(d)
At the point of projection
$r_A=\frac{u^2}{g \cos \theta}$
$r_H=\frac{u^2 \cos ^2 \theta}{g}$
Ratio, $\frac{r_A}{r_H}=\frac{\frac{u^2}{g \cos \theta}}{\frac{u^2 \cos ^2 \theta}{g}}=\frac{1}{\cos ^3 \theta}=\frac{r_A}{r_H}$
Standard 11
Physics