The period of oscillation of a simple pendulum is $T =2 \pi \sqrt{\frac{ L }{ g }} .$ Measured value of $ L $ is $1.0\, m$ from meter scale having a minimum division of $1 \,mm$ and time of one complete oscillation is $1.95\, s$ measured from stopwatch of $0.01 \,s$ resolution. The percentage error in the determination of $g$ will be ..... $\%.$
$1.13$
$1.03$
$1.33$
$1.30$
If $x = a -b,$ then percentage error in $x$ will be
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
In an experiment, the values of refractive indices of glass were found to be $1.54, 1.53,$$1.44,1.54,1.56$ and $1.45$ in successive measurements, then Mean absolute error is
We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be $2.63 \;s , 2.56 \;s , 2.42\; s , 2.71 \;s$ and $2.80 \;s$. Calculate the absolute errors, relative error or percentage error.