JEE Main Units and Measurements Previous year Question

31.(JEE Main 2019 (Online) 9th January Morning Slot )

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :

(A) 2.0 %

(B) 2.5 %

(C) 1.0 %

(D) 0.5 %

Correct answer is (C)

We know,

$R = \frac{ρ l}{A}$

and Volume (V) = A $l$

$\Rightarrow$    A $=$ $\frac{V}{l}$

$∴$     $R = \frac{ρ l^{2}}{v}$

$∴$     $\frac{Δ R}{R} = 2 \frac{Δ l}{l}$

$=$    2 $\times$ 0.5

$=$ 1%

32.(JEE Main 2018 (Online) 16th April Morning Slot )

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = $\frac{P^{3} Q^{2}}{\sqrt{R} S} .$

The maximum percentage error in the value of A will be :

(A) 6.0%

(B) 7.5%

(C) 8.5%

(D) 6.5%

Correct answer is (D)

Given,

A = $\frac{P^{3} Q^{2}}{\sqrt{R} S}$

$∴$ $\frac{Δ A}{A}$ = 3 $\frac{Δ P}{P}$ + 2 $\frac{Δ Q}{Q}$ + $\frac{1}{2}$ $\frac{Δ R}{R}$ + $\frac{Δ S}{S}$

Maximum percentage error in the value of A is

$\frac{Δ A}{A}$ $\times$ 100 = 3 $\times$ 0.5 + 2 $\times$ 1 + $\frac{1}{2}$ $\times$ 3 + 1 $\times$ 1.5

= 6.5 %

33.(JEE Main 2018 (Online) 16th April Morning Slot )

The relative uncertainly in the period of a satellite orbiting around the earth is 10^-2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

(A) 10^{$-$ 2}

(B) 2 $\times$ 10^{$-$ 2}

(C) 3 $\times$ 10^{$-$ 2}

(D) 6 $\times$ 10^{$-$ 2}

Correct answer is (B)

From kepler's law,

T = 2 $π$ $\sqrt{\frac{r^{3}}{G M}}$

$\Rightarrow$ T² = $\frac{4 π^{2}}{G M} r^{3}$

$\Rightarrow$ M = $\frac{4 π^{2}}{G} \times \frac{r^{3}}{T^{2}}$

$∴$ $\frac{Δ M}{M}$ = 2 $\frac{Δ T}{T}$ + 3 $\frac{Δ r}{r}$

as $\frac{Δ r}{r} ≃ 0$

$∴$ $| \frac{Δ M}{M} |$ = 2 $\frac{Δ T}{T}$ = 2 $\times$ 10^{$-$ 2}

34.(JEE Main 2018 (Offline) )

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:

(A) 6%

(B) 2.5%

(C) 3.5%

(D) 4.5%

Correct answer is (D)

Density of a material (d) = $\frac{M}{L^{3}}$

$∴$ Error in density, $\frac{Δ d}{d} = \frac{Δ M}{M} + 3 \frac{Δ L}{L}$

$\frac{Δ d}{d} \times 100 = \frac{Δ M}{M} \times 100 + 3 \frac{Δ L}{L} \times 100$

$\Rightarrow \frac{Δ d}{d} \times 100 = 1.5 % + 3 (1) %$ = 4.5 %

35.(JEE Main 2018 (Online) 15th April Morning Slot )

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

(A) $\frac{3}{2} α$

(B) $\frac{2}{3} α$

(C) $\frac{5}{2} α$

(D) $α$

Correct answer is (A)

Relative error in the surface are of the sphere,

$\frac{Δ S}{S}$ = 2 $\times$ $\frac{Δ r}{r}$ = $\propto$ (given)

Relative error in volume,

$\frac{Δ V}{V}$ = 3 $\times$ $\frac{Δ r}{r}$

= 3 $\times$ $\frac{1}{2}$ $\times$ $\frac{Δ S}{S}$

= $\frac{3}{2}$ $\times$ $\propto$

= $\frac{3}{2}$ $\propto$