37 The radius of a circle can be calculated from measurement

3.7. The radius of a circle can be calculated from measurements of the length L of a chord and the distance h from the chord to the circumference of the circle from the equation R L12h + h/2. Calculate the radius and its uncertainty from the following values of L and h. (a) L = (125.0 ± 5.0) cm, h (0.51 ± 0.22) cm (b) L = (125.0 ± 5.0) cm, h (57.4 ± 1.2) cm Was it necessary to use the second term to calculate R in both (a) and (b)? Explain. the answers are (a) 15300 6700 (b) 165+ 11 not sure how to get these answers though

Solution

Here for (a)

R=L²/2h + h/2

Putting L=125.0 ,h=0.51, we obtain,

R=15319

Now for the error part,

Erroe part of R=5²/2*0.22+0.22/2=57

Again for (b)

R=L²/2h + h/2

Putting L=125.0 ,h=57.4, we obtain,

R=165

Now for the error part,

Erroe part of R=5²/2*1.2+1.2/2=11

I think the answer of the error part you gave for part (a) is wrong.