Question

A particle moving along the circular path with a speed $v$ and its speed increases by $g$ in one second. If the radius of the circular path be $r$, then the net acceleration of the particle is:

• A. $\frac{v^{2}}{r}+g$
• B. $\frac{v^{2}}{r^{2}}+g^{2}$
• C. $\left(\frac{v^{2}}{r}+g\right)^{1 / 2}$
• D. $\left(\frac{v^{4}}{r^{2}}+g^{2}\right)^{1 / 2}$

Answer 1

Answer: (D)

Net acceleration $= \sqrt{a^{2}_{c} +a^{2}_{t}}$
In circular motion magnitude of velocity only changes by tangential acceleration.
tangential acceleration $= g$
$\therefore a = \sqrt{a^{2}_{c} +a^{2}_{t}}$
$a=\sqrt{\frac{v^{4}}{r^{2}} +g^{2}}$