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. $\left\lbrack \frac{v^{4}}{r^{2}} + g^{2} \right\rbrack^{\frac{1}{2}}$
• D. $\left\lbrack \frac{v^{2}}{r} + g \right\rbrack^{\frac{1}{2}}$

Answer 1

Answer: (C)

$\left\lbrack \frac{v^{4}}{r^{2}} + g^{2} \right\rbrack^{\frac{1}{2}}$

Answer 2

$a_{t} = g$ (given) and $a_{c} = \frac{v^{2}}{r}$ and $a_{N} = \sqrt{a_{t}^{2} + a_{c}^{2}} = \sqrt{\left( \frac{v^{2}}{r} \right)^{2} + g^{2}} = \sqrt{\frac{v^{4}}{r^{2}} + g^{2}}$