Length l , breadth b and thickness t of a block of wood were measured with help of a measuring scale

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1.Units, Dimensions and Measurement

easy

The length $l$, breadth b and thickness t of a block of wood were measured with the help of a measuring scale. The results with permissible errors are $l=15.12 \pm 0.01\; cm , t =5.28 \pm 0.01 \;cm$ $b =10.15 \pm 0.01\; cm$. The percentage error in volume upto proper significant figures is

$0.28$

$0.36$

$0.48$

$0.64$

Solution

Volume, $V = lbt$

The $\%$ error in volume $ = \,\,\frac{{\Delta \ell }}{\ell }\,\, \times \,\,\,100\,\, + \,\,\frac{{\Delta b}}{b}\,\, \times \,\,100\,\, + \frac{{\Delta t}}{t}\,\, \times \,\,100$

$ = \,\,\frac{{0.01}}{{15.12}}\,\, \times \,\,100\,\, + \;\,\frac{{0.01}}{{10.15}}\,\, \times \,100\,\, + \,\,\frac{{0.01}}{{5.28}}\,\, \times \,\,100$

$ = \,\,0.07\,\, + \;\,0.10\,\, + 0.19\,\, = \,\,0.36$

Standard 11

Physics

The least count of stop watch is $\frac{1}{5}\,second$. The time of $20$ oscillations of pendulum is measured to be $25\,seconds$. Then percentage error in the measurement of time will be………. $\%$

medium

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 ………. $\%$

medium

Following observations were taken with a vernier callipers while measuring the length of a cylinder

$3.29 \,cm, 3.28\, cm, 3.29 \,cm, 3.31 \,cm,$ $ 3.28\, cm, 3.27 \,cm, 3.29 \,cm, 3.30\, cm$

Then find Absolute error in forth and eighth observation

medium

A physical quantity is given by $X = {M^a}{L^b}{T^c}$. The percentage error in measurement of $M,L$ and $T$ are $\alpha ,\beta $ and $\gamma $ respectively. Then maximum percentage error in the quantity X is

easy

In the expression for time period $T$ of simple pendulum $T=2 \pi \sqrt{\frac{l}{g}}$, if the percentage error in time period $T$ and length $l$ are $2 \%$ and $2 \%$ respectively then percentage error in acceleration due to gravity $g$ is equal to ……… $\%$

medium

The length $l$, breadth b and thickness t of a block of wood were measured with the help of a measuring scale. The results with permissible errors are $l=15.12 \pm 0.01\; cm , t =5.28 \pm 0.01 \;cm$ $b =10.15 \pm 0.01\; cm$. The percentage error in volume upto proper significant figures is

Solution

Similar Questions

The least count of stop watch is $\frac{1}{5}\,second$. The time of $20$ oscillations of pendulum is measured to be $25\,seconds$. Then percentage error in the measurement of time will be………. $\%$

Following observations were taken with a vernier callipers while measuring the length of a cylinder $3.29 \,cm, 3.28\, cm, 3.29 \,cm, 3.31 \,cm,$ $ 3.28\, cm, 3.27 \,cm, 3.29 \,cm, 3.30\, cm$ Then find Absolute error in forth and eighth observation

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Following observations were taken with a vernier callipers while measuring the length of a cylinder

$3.29 \,cm, 3.28\, cm, 3.29 \,cm, 3.31 \,cm,$ $ 3.28\, cm, 3.27 \,cm, 3.29 \,cm, 3.30\, cm$

Then find Absolute error in forth and eighth observation