MHTCET 10 May 2024 Shift 2 Paper

Concept:Centripetal force required for uniform circular motion is $F = \frac{m v^{2}}{r}$. Since all three quantities change, we compare the new force with the original force to find the percentage change.Explanation:Let the initial values be $m$, $v$, and $r$.The initial centripetal force is:$$F_{\text{initial}} = \frac{m v^{2}}{r}$$Increasing each by $20\%$ gives:$$m' = 1.2m, \quad v' = 1.2v, \quad r' = 1.2r$$The new required force is:$$F_{\text{new}} = \frac{m' (v')^{2}}{r'} = \frac{(1.2m)(1.2v)^{2}}{1.2r}$$Simplify:$$F_{\text{new}} = \frac{1.2m \times 1.44v^{2}}{1.2r} = \frac{1.44m v^{2}}{r}$$So, $F_{\text{new}} = 1.44F_{\text{initial}}$.Therefore, the change in force is:$$\Delta F = F_{\text{new}} - F_{\text{initial}} = 1.44F_{\text{initial}} - F_{\text{initial}} = 0.44F_{\text{initial}}$$Thus, the percentage change in force is:$$\frac{\Delta F}{F_{\text{initial}}} \times 100\% = 0.44 \times 100\% = 44\%$$Answer:The necessary change in force is $44\%$, i.e., Option B.