Question

A particle is projected at angle $\theta$ with horizontal, with velocity $v_0$ at $t=0$. Find the radius of curvature at $t=0$.

• A. $v_0^2/g\cos \theta$
• B. $v_0^2\cos \theta /g$
• C. $(v_0\cos \theta {)}^2/g$
• D. $v_0^2/g$

Answer 1

The correct option is A $v_0^2/g\cos \theta$


The net acceleration of the particle during the motion is $g$.
Normal acceleration (centripetal acceleration) at $t=0,a_n=g\cos \theta$
Let the radius of curvature at $t=0$ be $R_0$.
Then, $a_n=\frac{v^2}{R}=\frac{v_0^2}{R_0}$
$\Rightarrow R_0=\frac{v_0^2}{a_n}=\frac{v_0^2}{g\cos \theta }$