In a certain experiments to measure the ratio of charge to mass of elementry particles, a surprising result was obtained in which two particle, a surprising result was obtained in which two particles moved in such a way that the distance between them always remained constant. It was also noticed that this two-particle system was isolated from all other particles and no force was acting on this system except the force between these two mases. After careful observation followed bu intensive calculation, it was deduced that velocity of these two particles was always opposite in direction and magnitude of velocity was `10^(3) ms^(-1) and 2 xx 10^(3) ms^(-1)` for first and second particle, respectively, and mass of these particles were `2 xx 10^(-30) kg and 10^(-30)kg`, respectively. Distance between them were 12Å(1Å = 10^(-`10)m).`
Acceleration of the first particle was

Options

A. zero
B. `4 xx 10^(16)ms^(-2)`
C. `2 xx 10^(16)ms^(-2)`
D. `2.5 xx 10^(15)ms^(-2)`

Answer

D

Explanation

The two particles move in different circles. The mutual interaction force provides the required centripetal force to the particle, as magnitude of the intersection force is same we get
`F_(12)=(m_(1)v_(1)^(2))/(r_(1))` and `F_(21)=(m_(2)v_(2)^(2))/(r_(2))`
`|vecF_(1)|=|vecF_(2)|` or `(m_(1)v_(1)^(2))/(r_(1))=(m_(2)v_(2)^(2))/(r_(2))`
putting values we get `r_(2)=2r_(1)`
Also, `r_(1)+r_(2)=12xx10^(-12)m` (given)
`r_(1)=4xx10^(-12)m,r_(2)=8xx10^(-12)m`
Acceleration of first particle `=(v_(1)^(2))/(r_(1))=((10^(3))^(2))/((4xx10^(-12)))`
`=2.5xx10^(15)ms^(-2)`