Question

A particle is projected at $t=0$ with velocity $u$ at angle $\theta $ with the horizontal. Then the ratio of the tangential acceleration and the radius of curvature at the point of projection is :-

• A. $\frac{g^{2} s i n 2 \theta }{u^{2}}$
• B. $\frac{2 g^{2} s i n \theta }{u^{2}}$
• C. $\frac{g^{2} s i n \theta }{u^{2}}$
• D. $\frac{g^{2} s i n 2 \theta }{2 u^{2}}$

Answer 1

Answer: (D)

$R.O.C.=\frac{u^{2}}{ gsin \theta }$
$a_{t}=gcos\theta $
so $\frac{a_{t}}{ R . O . C .}=\frac{g cos \theta }{u^{2}}\times g$