Question

A projectile is projected at some angle from the horizontal in a vertical plane. Then the angular momentum of the projectile about point of projection is proportional to $t^n$ where $t$ is time then $n$ is equal to:

• A. $1/2$
• B. $1$
• C. $1\frac{1}{2}$
• D. $2$

Answer 1

The correct option is D $2$

$V_x=ucos\theta$

$V_y=usin\theta -gt$

$x=V_{x}t=ucos\theta$ t

$y=usin\theta$ t - $\frac{1}{2}g{t}^2$

$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$

$(x\hat{j}+y\hat{j})\times (m{v}_x\hat{j}+m{v}_y\hat{j})$

$=m[x{v}_y-y{v}_x]\hat{k}$

$L=\left[\frac{-mu}{2}cos\theta g{t}^2\right]\hat{k}$

$L\propto t^2$