QJEEM20Ph0aee: JEE Main 2020 Physics - Class 11 JEEM20Ph0aee Solution: The density of a solid metal sphere is determined by measuring…

Question

Verified Solution • 2025–26 Session moderate

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is

\left( {{x \over {100}}} \right)

%. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is_______.

Accepted Answer

\rho

=

{M \over V}

=

{M \over {{4 \over 3}\pi {{\left( {{D \over 2}} \right)}^3}}}

\Rightarrow

\rho

=

{6 \over \pi }M{D^{ - 3}}

For maximum error

{{d\rho } \over \rho } \times 100 = {{dM} \over M} \times 100 + 3{{dD} \over D} \times 100

= 6 + 3

\times

1.5

= 10.5 %

=

\left( {{{1050} \over {100}}} \right)

%

\therefore

x = 1050

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