According to Joule's law of heating, heat produced $H = {I^2}\,Rt$, 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 error in the measurement of $H$ is
$ \pm 17\%$
$ \pm 16\%$
$ \pm 19\%$
$ \pm 25\%$
The radius of a sphere is measured to be $(7.50 \pm 0.85) \,cm .$ Suppose the percentage error in its volume is $x$. The value of $x$, to the nearest integer is .....$\%$
In order to determine the Young's Modulus of a wire of radius $0.2\, cm$ (measured using a scale of least count $=0.001\, cm )$ and length $1 \,m$ (measured using a scale of least count $=1\, mm$ ), a weight of mass $1\, kg$ (measured using a scale of least count $=1 \,g$ ) was hanged to get the elongation of $0.5\, cm$ (measured using a scale of least count $0.001\, cm$ ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)
The period of oscillation of a simple pendulum is $T=2\pi \sqrt {\frac{l}{g}} $. Measured value of $L$ is $20.0\; cm$ known to $1\; mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\ s$ using a wrist watch of $1\; s$ resolution. The accuracy in the determination of $g$ is ........ $\%$
The length of a cylinder is measured with a meter rod having least count $0.1\, cm$. Its diameter is measured with vernier calipers having least count $0.01\, cm$. Given that length is $5.0 \,cm$. and radius is $2.0 \,cm$. The percentage error in the calculated value of the volume will be ......... $\%$