JEE Main 2018 (Offline) | Units & Measurements Question 147 | Physics

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

2.5%

3.5%

4.5%

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MCQ (Single Correct Answer)

-1

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c.

Which of the following correctly gives the Planck length ?

G $$\hbar $$² c³

G² $$\hbar $$ c

$${G^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}{\hbar ^2}c$$

$${\left( {{{G\hbar } \over {{c^3}}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}$$

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MCQ (Single Correct Answer)

-1

The relative error in the determination of the surface area of sphere is $$\alpha $$. Then the relative error in the determination of its volume is :

$${3 \over 2}\alpha $$

$${2 \over 3}\alpha $$

$${5 \over 2}\alpha $$

$$\alpha $$

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MCQ (Single Correct Answer)

-1

In a screw gauge, $$5$$ complete rotations of the screw cause it to move a linear distance of $$0.25$$ $$cm.$$ There are $$100$$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $$4$$ main scale divisions and $$30$$ circular scale divisions. Assuming negligible zero error, the thickness of the wire is :

$$0.4300$$ $$cm$$

$$0.2150$$ $$cm$$

$$0.3150$$ $$cm$$

$$0.0430$$ $$cm$$

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