A body travels uniformly a distance of $ (13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3)\, s$. The velocity of the body within error limits is
$(3.45 \pm 0.2) ms^{-1}$
$(3.45 \pm 0.3) ms^{-1}$
$(3.45 \pm 0.4) ms^{-1}$
$(3.45 \pm 0.5) ms^{-1}$
In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is $10 \pm 0.1 \mathrm{~cm}$ and the distance of its real image from the lens is $20 \pm 0.2 \mathrm{~cm}$. The error in the determination of focal length of the lens is $n \%$. The value of $n$ is. . . . . . .
Explain least count and least count error. Write a note on least count error.
The relative error in the determination of the surface area of a sphere is $\alpha $. Then the relative error in the determination of its volume is
A physical quantity $A$ is dependent on other four physical quantities $p, q, r$ and $s$ as given below $A=\frac{\sqrt{pq}}{r^2s^3} .$ The percentage error of measurement in $p, q, r$ and $s$ $1\%,$ $3\%,\,\, 0.5\%$ and $0.33\%$ respectively, then the maximum percentage error in $A$ is .......... $\%$
A student determined Young's Modulus of elasticity using the formula $Y=\frac{M g L^{3}}{4 b d^{3} \delta} .$ The value of $g$ is taken to be $9.8 \,{m} / {s}^{2}$, without any significant error, his observation are as following.
Physical Quantity | Least count of the Equipment used for measurement | Observed value |
Mass $({M})$ | $1\; {g}$ | $2\; {kg}$ |
Length of bar $(L)$ | $1\; {mm}$ | $1 \;{m}$ |
Breadth of bar $(b)$ | $0.1\; {mm}$ | $4\; {cm}$ |
Thickness of bar $(d)$ | $0.01\; {mm}$ | $0.4 \;{cm}$ |
Depression $(\delta)$ | $0.01\; {mm}$ | $5 \;{mm}$ |
Then the fractional error in the measurement of ${Y}$ is