Physics
ASSERTION

The error in the measurement, of radius of the sphere is $$0.3$$% . The permissible error in its surface area is $$0.6$$%

REASON

The permissible error is calculated by the formula $$\dfrac {\Delta A}{A} = \dfrac {4\Delta r}{r}$$


ANSWER

Assertion is correct but Reason is incorrect


SOLUTION

Area of the sphere, $$A = 4\pi r^{2}$$

% error in area $$= 2 \times$$ % error in radius

i.e., $$\dfrac {\Delta A}{A} \times 100 = 2\times \dfrac {\Delta r}{r} \times 100$$

                           $$= 2\times 0.3$$ % $$= 0.6$$%

But $$\dfrac {\Delta A}{A} = 4 \dfrac {\Delta r}{r}$$ is false.

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Assertion & Reason Hard Published on 18th 08, 2020
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