Respuesta :
Answer:
Step-by-step explanation:
Given
acceleration of A is 4.9 times of acceleration of B
[tex]a_a=4.9\cdot a_b[/tex]
since it is a uniform acceleration therefore there is only centripetal acceleration
[tex]a=\frac{v^2}{r}[/tex]
[tex]\frac{v_a^2}{r_a}=4.9\times \frac{v_b^2}{r_b}[/tex]
[tex]\sqrt{4.9\times \frac{r_a}{r_b}}=\frac{v_a}{v_b}----1[/tex]
also Time-period of B is 2.4 times of A
[tex]T_b=2.4\cdot T_a[/tex]
[tex]2.4\times \frac{2\pi r_a}{v_a}=\frac{2\pi r_b}{v_b}[/tex]
[tex]2.4\times \frac{r_a}{v_a}=\frac{r_b}{v_b}[/tex]
[tex]2.4\times \frac{r_a}{r_b}=\frac{v_a}{v_b}----2[/tex]
substitute the value of 1 in 2
[tex]2.4\times \frac{r_a}{r_b}=\sqrt{4.9\cdot \frac{r_a}{r_b}}[/tex]
[tex]\sqrt{\frac{r_a}{r_b}}=\frac{\sqrt{4.9}}{2.4}[/tex]
[tex]\frac{r_a}{r_b}=\frac{4.9}{2.4^2}[/tex]
[tex]\frac{r_a}{r_b}=0.85[/tex]
The required ratio of radius of motion of particle A to that of B is closet to 0.85.
Given that,
The acceleration of particle A is 4.9 times that of particle B.
The period of particle B is 2.4 times the period of particle A.
We have to determine,
The ratio of the radius of the motion of particle A to that of particle B is closest to.
According to the question,
Let the particle first is A = x,
And particle second is B = y.
Acceleration of x is 4.9 times of acceleration of y.
Then,
[tex]a_x = 4.5 a_y[/tex]
Therefore, It is a uniform acceleration there is only centripetal acceleration.
Then,
[tex]a = \frac{v^{2} }{r} \\\\[/tex]
Putting the value of a from equation 1 to equation 2,
[tex]\frac{v_x^{2} }{r_y} = 4.9\times\frac{v_y^{2} }{r_x} \\\\= \frac{v_a^{2} }{v_x^{2} } = 4.9\times \frac{r_a}{r_b} \\\\= \frac{v_a}{v_b} = \sqrt{\frac{4.9 \times r_a}{r_b} }[/tex]
The time period of particle y is 2.4 times the period of particle x.
Then,
[tex]= T_y = 2.4\times T_x\\\\= \frac{2\pi r_y}{r_y} = 2.4 \times \frac{2\pi r_x}{v_x} \\\\= 2.4 \times \frac{r_x}{v_x}= \frac{r_y}{v_y}[/tex]
Putting the values from equation 3 to equation 4,
[tex]= 2.4\times\frac{r_x}{r_y} = \sqrt{\frac{4.9 \times r_x}{r_y} } \\\\= \sqrt{\frac{r_a}{r_b} } = \frac{\sqrt{4.9}}{2.4} \\\\= \frac{r_a}{r_b} = \frac{4.9}{(2.4)^{2} } \\\\= \frac{r_a}{r_b} = 0.85[/tex]
Hence, The required ratio of radius of motion of particle A to that of B is closet to 0.85.
For the more information about Motion click the link given below.
https://brainly.com/question/14772869
