If the length of a cylinder is $l = (4.00 \pm 0.01) \; cm$,radius $r = (0.250 \pm 0.001) \; cm$,and mass $m = 6.25 \pm 0.01 \; g$,calculate the percentage error in the determination of density.

$A$ projectile is thrown with velocity $U = 20 \ m/s \pm 5\%$ at an angle $60^{\circ}.$ If the projectile falls back on the ground at the same level,then which of the following values in $m$ cannot be a possible answer for the range?

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its moment of inertia $(I = M R^2)$ about its geometric axis. (in $\%$)

In an experiment for the measurement of $g$ using a simple pendulum,the time period was measured with an accuracy of $0.2 \%$ while the length was measured with an accuracy of $0.5 \%$. The percentage accuracy in the value of $g$ thus obtained is: (in $\%$)

The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$,respectively. The area of the floor is .................... $m^2$

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: