Question

UUESTIUN 2 The electrical force, W, experienced by two charged particles, 91 and 42, is given in terms of a known constant, k, and the distance of separation, r, as: W = kq1"q2/r^2 Assume that the charges and the distance are measured with a 10% uncertainty (e.g. Ur - 0.1*r). Which of the following would reduce the uncertainty in W the most? Decreasing the uncertainty in both charge measurements to 6%, while the uncertainty in distance is reduced to 8%. Decreasing the uncertainty in both charge measurements to 1%, while the uncertainty in distance is reduced to 9%. Neither. Both options decrease the uncertainty in W equally.

Answer 1

SOLUTION:

W=K .q₁ q2/r^{2 U_r}=0.1*r

     

(1) When uncertainty in charge= 6% i.e 1.06

  discharge= 8% i.e 1.08

(2) When uncertainty in charge = 1% i.e 1.01

   discharge= 9% i.e 1.09

from 1,2: value of w is (1) is on the initial assumption. Hence option 1 is correct.

So, option 1 reduces uncertainty.