Distance Between Two Points

Step 1: Applying Coulomb’s Law. The electrostatic force between two charges is given by: $F%20%3D%20%5Cfrac%7Bk%20q_1%20q_2%7D%7Br%5E2%7D$ where: - $k%20%3D%209%20%5Ctimes%2010%5E9$ N·m²/C² (Coulomb’s constant), - $q_1%20%3D%201%20%5Ctimes%2010%5E%7B-7%7D$ C, - $q_2%20%3D%202%20%5Ctimes%2010%5E%7B-7%7D$ C, - $r%20%3D%2020$ cm $%3D%200.2$ m.
Step 2: Substituting the values. $F%20%3D%20%5Cfrac%7B(9%20%5Ctimes%2010%5E9)%20(1%20%5Ctimes%2010%5E%7B-7%7D)%20(2%20%5Ctimes%2010%5E%7B-7%7D)%7D%7B(0.2)%5E2%7D$ $F%20%3D%20%5Cfrac%7B(9%20%5Ctimes%2010%5E9)%20%5Ctimes%20(2%20%5Ctimes%2010%5E%7B-14%7D)%7D%7B0.04%7D$ $F%20%3D%20%5Cfrac%7B18%20%5Ctimes%2010%5E%7B-5%7D%7D%7B4%20%5Ctimes%2010%5E%7B-2%7D%7D$ $F%20%3D%204.5%20%5Ctimes%2010%5E%7B-3%7D%20%7B%20N%7D$
Final Answer: $%5Cboxed%7B4.5%20%5Ctimes%2010%5E%7B-3%7D%20%7B%20N%7D%7D$

Step 1: {Given values}
We are given:

A%20%3D%201.0%20%5C%2Cm%20%5Cpm%200.2%20%5C%2Cm%2C%20%5Cquad%20B%20%3D%202.0%20%5C%2Cm%20%5Cpm%200.2%20%5C%2Cm

We define:

Y%20%3D%20%5Csqrt%7BAB%7D

Step 2: {Calculate the value of

Y

}

Y%20%3D%20%5Csqrt%7B(1.0)(2.0)%7D

%3D%20%5Csqrt%7B2.0%7D%20%3D%201.414%20%5C%2Cm

Step 3: {Determine the uncertainty in

Y

}
The formula for relative error propagation is:

%5Cfrac%7B%5CDelta%20Y%7D%7BY%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cleft(%20%5Cfrac%7B%5CDelta%20A%7D%7BA%7D%20%2B%20%5Cfrac%7B%5CDelta%20B%7D%7BB%7D%20%5Cright)

Substituting the given values:

%5Cfrac%7B%5CDelta%20Y%7D%7B1.4%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cleft(%20%5Cfrac%7B0.2%7D%7B1.0%7D%20%2B%20%5Cfrac%7B0.2%7D%7B2.0%7D%20%5Cright)

Step 4: {Simplify the expression}

%5Cfrac%7B%5CDelta%20Y%7D%7B1.4%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cleft(%200.2%20%2B%200.1%20%5Cright)

%5Cfrac%7B%5CDelta%20Y%7D%7B1.4%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%200.3%20%3D%200.15

%5CDelta%20Y%20%3D%200.15%20%5Ctimes%201.4%20%3D%200.21

Step 5: {Round off to one significant digit}

%5CDelta%20Y%20%3D%200.2%20%5C%2Cm

Thus, the final result is:

Y%20%3D%201.4%20%5C%2Cm%20%5Cpm%200.2%20%5C%2Cm

Step 6: {Verify the options}
Comparing with the given options, the correct answer is (D)

1.4%20%5C%2Cm%20%5Cpm%200.2%20%5C%2Cm

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Distance Between Two Points

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs