The ratio of the radius of the motion of particle A to that of particle B is 1:1
Solution:
Let v be the uniform circular motion, [tex]v=\frac{2 \times 3.14 \times R}{T} \rightarrow(1)[/tex]
centripetal acceleration be [tex]a=\frac{v^{2}}{R} \rightarrow(2)[/tex]
On substituting 1 in 2 we get, [tex]a=\frac{\left[\frac{2 \times 3.14 \times R}{T}\right]^{2}}{R}=\frac{2 \times 3.14 \times R}{T^{2}} \rightarrow (3)[/tex]
Given, acceleration of A = 6x; B = x Time taken by A = t ; B = 2.4t For particle A, substituting the values,
[tex]\begin{array}{l}{\Rightarrow 6 x=\frac{2 \times 3.14 \times R}{t^{2}}} \\\\ {\Rightarrow 6 x=\frac{6.28 R}{t^{2}}} \\\\ {\Rightarrow R=\frac{6}{6.28} \times x t^{2}} \\\\ {\Rightarrow R a=0.955 x t^{2}}\end{array}[/tex]
For particle B, substituting the values,
[tex]\begin{array}{l}{\Rightarrow x=2 \times 3.14 \times \frac{R}{(2.4 t)^{2}}} \\\\ {\Rightarrow x=\frac{6.28}{5.76} \times \frac{R}{t^{2}}} \\\\ {\Rightarrow R=\frac{5.76}{6.28} \times x t^{2}} \\\\ {R b=0.917 x t^{2}}\end{array}[/tex]
Therefore, the ratio of radii of A and B is Ra : Rb = 0.955 : 0:917 Approximately, it can be written as 1:1.
