Maharashtra Board Solutions for Chapter: Units and Measurements, Exercise 3: Exercises

Which of the following is not a fundamental unit?

$v=at+\frac{b}{t+c}+v_0$is a dimensionally valid equation, obtain the dimensional formula for a, b and c where v is velocity, t is time and $v_0$ is initial velocity

The length, breadth and thickness of a rectangular sheet of metal are $4.234\mathrm{m}$, $1.005\mathrm{m}$ and $2.01\mathrm{cm}$ respectively. Give the area and volume of the sheet to correct significant figures.

If the length of a cylinder is $L = (4.0\pm 0.001)\mathrm{cm}$, radius $R = (0.0250\pm 0.001) \mathrm{cm}$ and mass, $m = (6.25 \pm 0.01) \mathrm{g}$. Calculate percentage error in the determination of density.

When the planet Jupiter is at a distance of $824.7$ million kilometres from the earth, its angular diameter is measured to be $35.72"$ of arc. The diameter of Jupiter is $\left(y\times {10}^4\right) \mathrm{km}$. The value of number $y$ to the nearest integer is

(Take $\pi =3.14$)

If the formula for a physical quantity is $X=\frac{a^4{b}^3}{c^{1/3}{d}^{1/2}}$ and if the percentage error in measurement of a,b,c and d are$2\%, 3\%, 3\% \mathrm{and} 4\%$ respectively. Calculate percentage error in X.

Write down the no of significant figures in the following:

$0.003{\mathrm{m}}^2$ ,

$0.1250\frac{\mathrm{gm}}{{\mathrm{cm}}^2}$,

 $6.4\times \times {10}^6\mathrm{m}$,

 $1.6\times {10}^{-19}\mathrm{C}$,

 $9.1\times {10}^{-31}\mathrm{kg}$.

The diameter of a sphere is $2.14\mathrm{cm}$. Calculate the volume of the sphere to the correct number of a significant figure.