Units and Measu...

The number of significant figures in 0.06900 is:

The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is

The mass and volume of a body are 4.237 g and 2.5 \(cm^3\), respectively. The density of the material of the body in correct significant figures is:

The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give.

The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm respectively. The area of the sheet in appropriate significant figures and error is

Which of the following pairs of physical quantities does not have same dimensional formula?

Measure of two quantities along with the precision of respective measuring instrument is \(A = 2.5\ ms ^{-1} \pm 0.5\ ms^{-1}\) and \(B = 0.10\ s\pm 0.01 s\). the value of AB will be:

You measures two quantities as A = (1.0 \(\pm\) 0.2) m, B = 2.0 m \(\pm\) 0.2 m. we report correct value of \(\sqrt{AB}\) as:

Which of the following measurement is most precise?

The mean length of an object is 5 cm. Which of the following measurement is most accurate?

Young’s modulus of steel is \(1.9\times 10^{11} N/m^2 \). When expressed in CGS units of \(dyne/cm^2\) . It will be equal to (1N=\(10 ^5\) dynes, and 1 \(m^2\) =\(10 ^4\) \(cm^2\)).

If the momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has dimensional formula.

On the basis of dimensions, decide which of the following relations for the displacement of particle undergoing simple harmonic motion is not correct.

(a) y = a sin \(({2\pi t\over T})\)

(b) y = a sin vt

(c) y = \({a\over T}\, sin({t\over a})\)

(d) y = \(a\sqrt2[sin{2\pi t\over T}-cos{2\pi t\over T}]\)

P,Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

(a) \((P-Q)\over R\)

(b) \( (PQ-R)\)

(c) \(PQ\over R\)

(d) \(PR-Q^2\over R\)

(e) \((R+Q)\over R\)

Photon is quantum of radiation with energy E = hv, where v is frequency and h is Planck’s constant .The dimensions of h are the same as that of:

(a) Linear impulse

(b) Angular impulse

(c) Linear momentum

(d) Angular momentum

If the Planck’s constant (h) and the speed of light in vacuum (c) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three choosen fundamental quantities.

(a) Mass of electron \((m_e ) \)

(b) Universal gravitational constant (G)

(c) Charge of electron (e)

(d) Mass of proton \((m_p)\)

Which of the following ratios express pressure?

(a) Force/Area

(b) Energy/volume

(c) Energy/Area

(d) Force/Volume

Which of the following are not unit of time?

(a) Second

(b) Parsec

(c) Year

(d) Light year

Fill in the blanks

(a) The volume of a cube of side 1 cm is equal to ..... \(m^3\).

(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ..... \(mm^2\) .

(c) A vehicle moving with a speed of 18 \(kmh^{–1}\) covers .... m in 1 s.

(d) The relative density of lead is 11.3. Its density is ....... \(g\ cm^{–3}\) or ...... \(kg\ m^{–3}\).

Fill in the blanks by suitable conversion of units :

(a) \(1\, kg\, m^2\, s^{–2} =\, ....g\, cm^2\, s^{–2}\)

(b) 1 m = ........ ly (light year)

(c) 3.0 \(ms^{–2}\) = ..... \(kmh^{–2 }\)

(d) G = 6.67 x \(10^{–11} Nm^2 kg^{–2}\) = .... \(cm^3 s^{–2} g^{–1}\)