The mean time period of second's pendulum is 2.00s and mean absolute error in the time period is 0.05s. To express maximum estimate of error, the time period should be written as

(1) (2.00 ± 0.01) s

(2) (2.00 + 0.025) s

(3) (2.00 ± 0.05) s

(4) (2.00 ± 0.10) s

A body travels uniformly a distance of (13.8 $\pm$ 0.2) m in a time (4.0 ± 0.3) sec. The velocity of the body within error limits is:

1. (3.45 ± 0.2) ms^-1

2. (3.45 ± 0.3) ms^-1

3. (3.45 ± 0.4) ms^-1

4. (3.45 ± 0.5) ms^-1

The unit of percentage error is

(1) Same as that of physical quantity

(2) Different from that of physical quantity

(3) Percentage error is unit less

(4) Errors have got their own units which are different from that of physical quantity measured

Accuracy of measurement is determined by

(1) Absolute error

(2) Percentage error

(3) Both

(4) None of these

A thin copper wire of length l metre increases in length by 2% when heated through 10ºC. What is the percentage increase in area when a square copper sheet of length l metre is heated through 10ºC

(1) 4%

(2) 8%

(3) 16%

(4) None of the above

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 m 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.

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) ($b_1+c_1+d_1+e_1$)%

(2) ($b_1+c_1-d_1-e_1$)%

(3) ($\alpha b_1+\beta c_1-\gamma d_1-\delta e_1$)%

(4) ($\alpha b_1+\beta c_1+\gamma d_1+\delta e_1$)%

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

The periods of oscillation of a simple pendulum in an experiment are recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s, and 2.80 s respectively. The average absolute error will be:

1. 0.1 s

2. 0.11 s

3. 0.01 s

4. 1.0 s