Unreasonable Results (a) Two 0.500 g raindrops in a thunderhead are 1.00 cm apart when they each acquire 1.00 mC charges. Find their acceleration. (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?
Solution: Step 1 (a) In the above question they have given, Two 0.500 g raindrops in a thunderhead are 1.00 cm apart when they each acquire 1.00 mC charges. Then we need to find their acceleration So first we mentioned coulomb’s law to find the electrostatic force between rains drop. kqq F = r 2 Here, F is the force of attraction, k is the constant whose value is equal and is charge. Now this electrostatic force must be equal to Newton’s force acting on each rain drop because the accelerated generated is the result of electrostatic force. Therefore the Newton’s second law of force is, F =Gma Here, m is the mass of rain drop and a is the acceleration of each drop. Step 2 Therefore, calculate the above two equation is F = F G F = ma ( we al ready know the value of F G =ma ) kqq Substitute the value of F = r 2 in the above equation is kq 2 r2 = ma kq 2 ma = 2 r kq 2 a = 2 mr Step 3 2 Substitu te, 9.0 × 10 9 Nm 2 for k, .50 g f or m, (10 cm) f or r, and 1.0 ×10 C for q C the above equation we get as, (9.0 ×109 Nm 2)(1.0 ×103 C) 2 a = C 2 (0.50 g)(0.01 m) 2 (9.0 ×109 Nm 2)(1.0 ×103 C) 2 a = C 3 (0.50 g× 101 gg)(0.01 m) 2 11 2 a = 1.80 × 10 m/s Therefore, the magnitude of net acceleration is 1.80 × 10 m/s . 11 2