The density of a solid sphere is determined by measuring its mass and radius. The mass is measured using a balance with a least count of 1\ g and is found to be 100\ g . The radius is measured using vernier calipers and

Question

Quantrex Academy · Accepted Answer

Correct answer: A. 0.01\ cm

The density of a solid sphere is given by the formula:

\rho = \dfrac{M}{V} = \dfrac{M}{\dfrac{4}{3}\pi R^3}

The maximum percentage error in the density is given by:

\dfrac{\Delta \rho}{\rho} \times 100 = \dfrac{\Delta M}{M} \times 100 + 3\dfrac{\Delta R}{R} \times 100

Given values:

\dfrac{\Delta \rho}{\rho} \times 100 = 2.5\%

M = 100\ \text{g}

\Delta M = 1\ \text{g}

(least count of the balance)

R = 2.00\ \text{cm}

\Delta R

is the least count of the vernier calipers.

Substituting the given values into the error equation:

2.5 = \left(\dfrac{1}{100}\right) \times 100 + 3 \times \left(\dfrac{\Delta R}{2.00}\right) \times 100

2.5 = 1 + 150 \Delta R

1.5 = 150 \Delta R

\Delta R = \dfrac{1.5}{150} = 0.01\ \text{cm}

Answer:

0.01\ \text{cm}

The density of a solid sphere is determined by measuring its mass...

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