The period of oscillation of a simple pendulum is given by \(T = 2\pi \sqrt{\frac{L}{g}}\) where \(L\) is about \(100~\text{cm}\) and is known to have \(1~\text{mm}\) accuracy. The period is about \(2~\text{s}\). The time of \(100\) oscillations is measured by a stopwatch of least count \(0.1~\text{s}\). The percentage error in \(g\) is:
1. \(0.1\%\)
2. \(1\%\)
3. \(0.2\%\)
4. \(0.8\%\)

The percentage errors in the measurement of mass and speed are \(2\%\) and \(3\%\) respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed:

What is the number of significant figures in \(0.310\times 10^{3}?\)

Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is 

(1) 1%

(2) 3%

(3) 5%

(4) 7%

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