Question

The radius of sphere 'r' is measured with vernier callipers as(r + ∆r)= (2.25 +0.01) cm. Calculate the volume of sphere. Answer should be this (47.7+0.6) cm.I need valid and proper explanation numerically.​

Answer 1

Least count, LC=0.01cm

Here the negative zero error of callipers =5×0.01=0.05cm and it should be added to final reading.

Main scale reading, MSR=2.4cm and VSD=6

So total reading means the diameter of sphere R=MSR+(VSD×LC)+ zero error =2.4+(6×0.01)+0.05=2.51 cm

Answer 2

radius r= (2.25 +- 0.01) cm

volume V= 4/3. × 22/7. × (2.25)^3

=47.7 cm^3

in such problems where we have terms raised to certain power we calculate the uncertainty as:

v=4/3πr^3

∆v/v. = 3 × ∆r/r    (uncertainty = error)

∆v/v = 3× 0.01/2.25

∆v = 3× 1/2.25 × v

∆v = 3×1/2.25 × 47.7

∆v= 0.636 cm^3

Thus, V (volume) = (47.7+-0.6) cm^3