Answer:
[tex]\dfrac{R_A}{R_B}=0.85[/tex]
Explanation:
given,
Acceleration of Particle A = 4.9 times particle B
Period of particle B = 2.4 times Period of A
Ratio of radius of the motion of particle A to B = ?
For Particle A
[tex]a_A = \dfrac{v_A^2}{R_A}[/tex]
For Particle B
[tex]a_B = \dfrac{v_B^2}{R_B}[/tex]
Form the question
[tex]\dfrac{a_A}{a_B}=4.9[/tex]
[tex]\dfrac{v_A^2R_B}{v_B^2R_A}=4.9[/tex]
and
[tex]\dfrac{T_B}{T_A}=2.4=\dfrac{R_Bv_A}{v_BR_A}[/tex]
[tex]5.76 = \dfrac{R_B^2v_A^2}{v_B^2R_A^2}[/tex]
[tex]5.76= 4.9\times \dfrac{R_B}{R_A}[/tex]
[tex]\dfrac{R_A}{R_B}=0.85[/tex]
Hence, the ration of the radius of the Particle A that of B = 0.85.
