The pressure on a square plate is measured by measuring the force acting on the plate and the length of the sides of the plate. If the maximum percentage error in the measurement of force and length are $4 \%$ and $2 \%$ respectively,what is the percentage error in the measurement of pressure (in $\%$)?

The period of an oscillating simple pendulum is $T = 2 \pi \sqrt{\frac{\ell}{g}}$,where the length $\ell = 100 \text{ cm}$ with an error of $1 \text{ mm}$. The period $T = 2 \text{ s}$. The time for $100$ oscillations is measured by a stopwatch with a least count of $0.1 \text{ s}$. The percentage error in the gravitational acceleration $g$ is: (in $\%$)

The measured value of the length of a simple pendulum is $20 \ cm$ with $2 \ mm$ accuracy. The time for $50$ oscillations was measured to be $40 \ s$ with $1 \ s$ resolution. From these measurements,the accuracy in the measurement of acceleration due to gravity is $N \%$. The value of $N$ is:

Two resistors of resistances $R_{1} = 100 \pm 3 \ \Omega$ and $R_{2} = 200 \pm 4 \ \Omega$ are connected $(a)$ in series,$(b)$ in parallel. Find the equivalent resistance of the $(a)$ series combination,$(b)$ parallel combination. Use for $(a)$ the relation $R = R_{1} + R_{2}$ and for $(b)$ $\frac{1}{R^{\prime}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$ and $\frac{\Delta R^{\prime}}{R^{\prime 2}} = \frac{\Delta R_{1}}{R_{1}^{2}} + \frac{\Delta R_{2}}{R_{2}^{2}}$.

The mass of an empty beaker is $(10.1 \pm 0.1) \, g$. When it is completely filled with a liquid,its mass becomes $(17.3 \pm 0.1) \, g$. What is the best value for the mass of the liquid within the possible limits of accuracy?

The time period of a simple harmonic oscillator is $T = 2 \pi \sqrt{\frac{m}{k}}$. The measured value of mass $(m)$ of the object is $10 \ g$ with an accuracy of $10 \ mg$,and the time for $50$ oscillations of the spring is found to be $60 \ s$ using a watch of $2 \ s$ resolution. The percentage error in the determination of the spring constant $(k)$ is . . . . . . %.