Two equally charged particles held 35 mm apart are released...

Two equally charged particles, held 3.5 mm apart, are released from rest. The initial magnitude of the acceleration of the first particle is observed to be 1.112×10-14 m/s2 and that of the second to be 8.925×10-15 m/s2. If the mass of the first particle is 61.0 µg, what is the mass of the second particle?

Transcript

00:01 Hello students.

00:02 In this question we are provided with two equally charged particles having different masses m1 and m2 they are separated by a distance d is equal to 3 .2 multiplied with 10 to the power minus 3 meters and it is given that both of this masses are accelerating with different speeds so we can here see in the figure this is accelerating at the rate of 9 .1 meter per second square and this is accelerating at 7 .1 meter per second square so if we are provided with the mass of m1 we first need to find a mass of m2 and then we also need to find the charge on each of the mass and since they are both equally charged so we can just find the charge q so here we'll start with the first part in the first part we are asked to find out what will be the mass of the second body now since these are equally charged particles so there will be a repulsive force acting on each other so on m2 there will be a repulsive force f1 acting because of m1 and on m1 there will be a refusive force force f2 acting because of m2 and here f1 is equal to f2 and that is equal to f2 and that will be equal to k times q squared divided by d square q square divided by d square and this is the repulsive force this is the repulsive force that is acting on each of the charge particle because of the other particle and this repulsive force will be responsible of producing the acceleration on each of the body.

01:39 The repulsive force f1 will produce the acceleration in a2, whereas the repulsive force f2 will produce the acceleration in a1.

01:53 So what it actually means is that now we know that both of this will be acted upon by a repulsive force f.

02:02 And we know that force is equal to mass times acceleration.

02:08 So what we can say that, the repulsive force acting on m2, that is f, will be equal to m2 times acceleration a 2, and f is also equal to m1 multiplied with a 1.

02:23 So if we take the ratio of both the sides, we get that f by m2 divided by f by if we take the ratio by m1 this would be equal to a 2 divided by a 1 so f and f and f gets cancelled with each other and we get that m1 by m2 is equal to a 2 by a 1 and since we need to find out the mass m 2 m 2 will be simply equal to m1 multiplied sorry we need to find the mass m1 so m1 is equal m2 is equal to m1 multiplied with so this would be equal to a1 divided by a 2 so on putting the values of each of the variables in the in the formula we find out that the mass of the second body m2 is equal to so m1 is equal to 5 multiplied with 10 to the power minus 7 kg multiplied with a 1 a 1 is 7 .1 and a 2 is 9 .1 and this will be in kg and on calculating we get m2 is equal to 3 .9 applied with 10 to the power minus 7 kg so this is the mass of body m2 now we also need to find out the charge on each of the particle we need to find out what charge that is each of the particle carry and we're going to use the same formula to find that out as well so here we found out that so here we found out that the columbic force of attraction f is equal to m1 a1 and this is also equal to k k k k square by d square so what we can say that q square will be equal to m1 a1 multiplied with d squared divided by k this implies that q will be equal to that is a charge on each of the particle would simply be equal to root over of m1 a1 multiplied with d squared divided by k so putting the values of all the variables in this formula, we get that...

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