If there is an error of $1\%$ in calculation of mass of disc and $1.5\%$ error in radius, then $\%$ error in moment of inertia about an axis tangent to disc is .......... $\%$
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A student performs an experiment of measuring the thickness of a slab with a vernier calliper whose $50$ divisions of the vernier scale are equal to $49$ divisions of the main scale. He noted that zero of the vernier scale is between $7.00\; cm$ and $7.05 \;cm$ mark of the main scale and $23^rd$ division of the vernier scale exactly coincides with the main scale. The measured value of the thickness of the given slab using the calliper will be
Number of particles is given by $n = - D\frac{{{n_2} - {n_1}}}{{{x_2} - {x_1}}}$ crossing a unit area perpendicular to X-axis in unit time, where ${n_1}$ and ${n_2}$ are number of particles per unit volume for the value of $x$ meant to ${x_2}$ and ${x_1}$. Find dimensions of $D$ called as diffusion constant
Measure of two quantities along with the precision of respective measuring instrument $A = 2.5\,m{s^{ - 1}} \pm 0.5\,m{s^{ - 1}}$, $B = 0.10\,s \pm 0.01\,s$ The value of $AB$ will be
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, then find the maximum percentage error in the measurement of its angular momentum $(J=I \omega)$ about geometrical axis.
$Assertion$ : The number of significant figures depends on the least count of measuring instrument.
$Reason$ : Significant figures define the accuracy of measuring instrument.
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 .....$\%$
An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is