Question

If mass speed and radius of rotation of a body moving in a circular path are all increased by 50%, the necessary force required to maintain the body moving in the circular path will have to be increased by

• A. 225%
• B. 125%
• C. 150%
• D. 100%

Answer 1

Answer: (B)

125%

Answer 2

Centripetal force $F = \frac{mv^{2}}{r}$

If m, v and r are increased by 50% then let new force $F' = \frac{\left( m + \frac{m}{2} \right)\left( v + \frac{v}{2} \right)^{2}}{\left( r + \frac{r}{2} \right)}$ $= \frac{9}{4}\frac{mv^{2}}{r}$ $= \frac{9}{4}F$

Percentage increase in force $\frac{\Delta F}{F} \times 100 = \frac{F' - F}{F} \times 100\% = \frac{500}{4}\% = 125\%$