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

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

The length of a cylinder is measured with a meter rod having the least count of \(0.1~\text{cm}\). Its diameter is measured with vernier callipers having the least count of \(0.01~\text{cm}\). Given that the length is \(5.0~\text{cm}\) and the radius is \(2.0~\text{cm}\). The percentage error in the calculated value of the volume will be:

In an experiment, the following observations were recorded: initial length \(L =2.820~\text{m}\), mass \(M = 3.00~\text{kg}\), change in length \(l = 0.087~\text{cm}\), diameter \(D = 0.041~\text{cm}\). Taking \(g = 9.81~\text{m/s}^2\) and using the formula, \(Y = \frac{4MgL}{\pi D^2l},\) the maximum permissible error in \(Y \) will be:
1. \(7.96\%\)
2. \(4.56\%\)
3. \(6.50\%\)
4. \(8.42\%\)

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%

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

(1) 25%

(2) 50%

(3) 100%

(4) 125%

A physical quantity \(P\) is given by \(P=\dfrac{A^3 B^{1/2}}{C^{-4}D^{3/2}}.\) The quantity which contributes the maximum percentage error in \(P\) is: