An electron in a research apparatus follows a circle path. On the electron’s first circuit of the apparatus, its speed is v0 and the radius of its circular path is R. Each time it makes on circuit, it passes a short region where it receives a “kick” and gains an additional speed of <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>.</mo> </mrow> </math> The electron follows a circular path such that the magnitude of its acceleration is always the same. What is the radius of the circular path after the electron has received 10 kicks?

a = v 0 2 R after 10 kicks, v = v 0 + 1 0 v 0 1 0 0 = 1 . 1 v 0 ⇒ R 1 = 1 . 2 1 R

An electron in a research apparatus follows a circle path. On the electron’s first circuit of the apparatus, its speed is v0 and the radius of its circular path is R. Each time it makes on circuit, it passes a short region where it receives a “kick” and gains an additional speed of <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>.</mo> </mrow> </math> &nbsp;The electron follows a circular path such that the magnitude of its acceleration is always the same. What is the radius of the circular path after the electron has received 10 kicks?

Ask & Answer Question

Option 1 -

$\frac{R}{1.1}$

Option 2 -

1.1

Option 3 -

1.21

Option 4 -

$\frac{R}{1.21}$

2 Views | Posted a month ago

Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

$a = \frac{v_{0}^{2}}{R}$ $\frac{_{}^{}}{}$

after 10 kicks, $v = v_{0} + \frac{10 v_{0}}{100} = 1.1 v_{0}$ $_{} \frac{_{}}{}_{}$

$\Rightarrow R_{1} = 1.21 R$