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:
1. \(2.5\%\)
2. \(3.5\%\)
3. \(4.5\%\)
4. \(6\%\)

In a simple pendulum experiment for determination of acceleration due to gravity (\(g\)), time taken for \(20\) oscillations is measured by using a watch of \(1\) second least count. The mean value of time taken comes out to be \(30~\text{s}\). The length of pendulum is measured by using a meter scale of least count \(1~\text{mm}\) and the value obtained is \(55.0~\text{cm}\). The percentage error in the determination of \(g\) is close to:
1. \(0.7\%\)
2. \(6.8\%\)
3. \(0.2\%\)
4. \(3.5\%\)

The period of oscillation on a simple pendulum is \(T=2\pi\sqrt{\frac{L}{g}}\). The measured value of \(L\) is \(20.0~\text{cm}\) known to have \(1~\text{mm}\) accuracy and the time for \(100\) oscillations of the pendulum is found to be \(90~\text{s}\) using a wristwatch of \(1~\text{s}\) resolution. The accuracy in the determination of \(g\) is:
1. \(2\%\)
2. \(3\%\)
3. \(1\%\)
4. \(5\%\)

The following observations were taken to determine the surface tension \(T\) of water by the capillary method:
diameter of the capillary, \(D=1.25 \times 10^{-2} ~\text{m}\)
rise of water, \(h=1.45\times 10^{-2}~\text{m}\)
Using \(g= 9.80~\text{m/s}^2\) and the simplified relation, the possible error in surface tension is closest to: 
1. \(0.15\%\)
2. \(1.5\%\)
3. \(2.4\%\)
4. \(10\%\)

The current-voltage relation of the diode is given by \(I=(e^{1000V/T}-1)~\text{mA}\), where the applied voltage \(V\) is in volts and the temperature \(T\) is in degree Kelvin. If a student makes an error measuring \(\pm ~0.01~\text{V}\) while measuring the current of \(5~\text{mA}\) at \(300~\text{K}\), what will be the error in the value of current in \(\text{mA}\)?
1. \(0.02~\text{mA}\)
2. \(0.5~\text{mA}\)
3. \(0.05~\text{mA}\)
4. \(0.2~\text{mA}\)