Question

A ball is made of a long string of thickness about 2 mm. The radius of the ball is 10 cm. Estimate the length of the string. Point out the possible errors in your calculation.

Answer 1

Solution to #85710, Physics/Classical mechanics

Comparing the total volume occupied by the string with the volume of ball gives rise to relation as

$$L = \frac {4 R ^ {3}}{d ^ {2}}$$

Where L is the length of string

R is the radius of ball=10cm=0.10m

d is the thickness of string=2mm=2/1000 m

Dimension should have same units

$$L = \frac {4 R ^ {3}}{d ^ {2}}$$ $$L = \frac {4 (0 . 1) ^ {3}}{\left(2 / 1 0 0 0\right) ^ {2}}$$ $$L = \frac {0 . 0 0 4}{4 (1 0) ^ {- 6}}$$ $$L = 1 0 0 0 m$$ $$\mathrm {L} = 1 \mathrm {k m}$$

Possible error: While deriving the formula

i) Calculation is based on assumption of ball is spherical

ii) It is possible that strings in the ball is not closely packed and have gaps between uncountable gaps between adjacent sections of the string

iii) The value of pie is assume as 3.00 but actual is 3.14

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