The two specific heat capacities of a gas are measured as $C_P = (12.28 \pm 0.2) \text{ units}$ and $C_V = (3.97 \pm 0.3) \text{ units}$. Find the value of the gas constant $(R)$.

The distance $s$ travelled by a particle in time $t$ is $s = ut - \frac{1}{2} gt^2$. The initial velocity of the particle was measured to be $u = 1.11 \pm 0.01 \, m/s$ and the time interval of the experiment was $t = 1.01 \pm 0.1 \, s$. The acceleration was taken to be $g = 9.8 \pm 0.1 \, m/s^2$. With these measurements,the student estimates the total distance travelled. How should the student report the result?

The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$ respectively. What will be the maximum percentage error in the estimation of the kinetic energy obtained by measuring mass and speed?

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 $1\,s$ least count. The mean value of time taken comes out to be $30\,s$. The length of the pendulum is measured by using a meter scale of least count $1\,mm$ and the value obtained is $55.0\,cm$. The percentage error in the determination of $g$ is close to ........... $\%$

The percentage errors in measurements of mass and speed of a body are $2 \%$ and $3 \%$ respectively. What is the percentage error in kinetic energy of the body (in $\%$)?

Explain the statement: "The accuracy of a measurement cannot be determined by absolute error,but only by percentage error."