To find the spring constant $(k)$ of a spring experimentally,a student commits $2 \%$ positive error in the measurement of time and $1 \%$ negative error in the measurement of mass. The percentage error in determining the value of $k$ is (in $\%$)

Resistance of a rod is calculated by measuring its length with the help of a meter scale of least count $1 \ mm$. Its radius is measured with the help of a screw gauge having $50$ divisions on the circular scale and a pitch of $1 \ mm$. Resistivity of the material is exact. The length of the wire is found to be $20 \ cm$ and the diameter of the wire is $4 \ mm$. Find the percentage error in the calculation of resistance.

If the error in measuring the diameter of a circle is $4\%$,the error in the radius of the circle would be (in $\%$)

According to Joule's law of heating,heat produced $H = I^2Rt$,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 the error in the measurement of $H$ is:

Calculate the mean percentage error in five observations: $80.0, 80.5, 81.0, 81.5, 82.0$. (in $\%$)

The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$,the percentage error in calculated volume of cylinder is ............. $\%$