In the context of the accuracy of measurement and significant figures in expressing the results of the experiment, which of the following is/are correct?

(1) Out of the two measurements 50.14 cm and 0.00025 Amperes, the first one has greater accuracy.

(2) If one travels 478 km by rail and 397 by road, the total distance traveled is 478 km.

1. Only (1) is correct

2. Only (2) is correct

3. Both are correct

4. None of them is correct.

Concept Questions :-

Significant Figures
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Difficulty Level:

A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = ${b}^{\alpha }{c}^{\beta }/{d}^{\gamma }{e}^{\delta }$. If the maximum errors in the measurement of b, c, d and e are b1%, c1%, d1% and e1%, then the maximum error in the value of a determined by the experiment is

(1) (${b}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{c}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{d}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{e}_{1}$)%

(2) (${b}_{1\text{\hspace{0.17em}}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{c}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{d}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{e}_{1}$)%

(3) ($\alpha {b}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\beta {c}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\gamma {d}_{1}\text{\hspace{0.17em}}-\delta {e}_{1}$)%

(4) ($\alpha {b}_{1}+\text{\hspace{0.17em}}\beta {c}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\gamma {d}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\delta {e}_{1}$)%

Concept Questions :-

Errors
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Difficulty Level:

The relative density of material of a body is found by weighing it first in air and then in water. If the weight in air is (5.00 ± 0.05) Newton and weight in water is (4.00 ± 0.05) Newton. Then the relative density along with the maximum permissible percentage error is

(1) 5.0 ± 11%

(2) 5.0 ± 1%

(3) 5.0 ± 6%

(4) 1.25 ± 5%

Concept Questions :-

Errors
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Difficulty Level:

The resistance R = $\frac{V}{i}$ where V= 100 ± 5 volts and i = 10 ± 0.2 amperes. What is the total error in R

(1) 5%

(2) 7%

(3) 5.2%

(4) $\frac{5}{2}$%

Concept Questions :-

Errors
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Difficulty Level:

The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s respectively. The average absolute error is

(1) 0.1 s

(2) 0.11 s

(3) 0.01 s

(4) 1.0 s

Concept Questions :-

Errors
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Difficulty Level:

The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with vernier calipers having least count 0.01 cm. Given that length is 5.0 cm. and radius is 2.0 cm. The percentage error in the calculated value of the volume will be

(1) 1%

(2) 2%

(3) 3%

(4) 4%

Concept Questions :-

Errors
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Difficulty Level:

In an experiment, the following observation's were recorded : L = 2.820 m, M = 3.00 kg, l = 0.087 cm, Diameter D = 0.041 cm Taking g = 9.81 m/s2 using the formula , Y = $\frac{4MgL}{\pi {D}^{2}l}$, the maximum permissible error in Y is

(1) 7.96%

(2) 4.56%

(3) 6.50%

(4) 8.42%

Concept Questions :-

Errors
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Difficulty Level:

According to Joule's law of heating, heat produced H = I2Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively then error in the measurement of H is

(1) ± 17%

(2) ± 16%

(3) ± 19%

(4) ± 25%

Concept Questions :-

Errors
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Difficulty Level:

If there is a positive error of 50% in the measurement of velocity of a body, then the error in the measurement of kinetic energy is

(1) 25%

(2) 50%

(3) 100%

(4) 125%

Concept Questions :-

Errors
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Difficulty Level:

A physical quantity P is given by P = $\frac{{A}^{3}{B}^{\frac{1}{2}}}{{C}^{-4}{D}^{\frac{3}{2}}}$. The quantity which brings in the maximum percentage error in P is

(1) A

(2) B

(3) C

(4) D

Concept Questions :-

Errors