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3.2 , motion in plane — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
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
    $\frac{1}{\sin ^3 \theta}$
  • ✓
    $\frac{1}{\cos ^3 \theta}$
✓

Answer

Correct option: D.
$\frac{1}{\cos ^3 \theta}$
d
(d)

At the point of projection

$r_A=\frac{u^2}{g \cos \theta}$

$r_H=\frac{u^2 \cos ^2 \theta}{g}$

Ratio, $\frac{r_A}{r_H}=\frac{\frac{u^2}{g \cos \theta}}{\frac{u^2 \cos ^2 \theta}{g}}=\frac{1}{\cos ^3 \theta}=\frac{r_A}{r_H}$

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