__Dimensions and Measurement__

Q1. A New unit of length is chosen such that the speed of
light in vacuum is unity. What is the distance between the sun and the earth in
terms of the new unit if light takes 8 min and 20 s to cover this distance.

Q2. If x = a + bt + ct2, where x is in metre and in seconds, what is the unit of c ?

Q3. What is the difference between mN, Nm and nm ?

Q4. The radius of atom is of the order of 1A

^{o }& radius of Nucleus is of the order of fermi. How many magnitudes higher is the volume of the atom as compared to the volume of nucleus ?
Q5. How many kg make 1 unified atomic mass unit?

Q6. Name same physical quantities that have same
dimension.

Q7. Name the physical quantities that have dimensional
formula [ML

^{–1}T^{–2}]
Q8. Give two examples of dimension less variables.

Q9. State the number of significant figures in

(i) 0.007m

^{2}(ii) 2.64 × 10^{24 }kg
(iii) 0.2370 g cm

^{–3}(iv) 0.2300m(v) 86400 (vi) 86400m
Q10. Given relative error in the measurement of length is
.02, what is thepercentage error?

Q11. A physical quantity P is related to four observables
a, b, c and d as

follows :P = a

^{3}b^{2}/ ( cd) The percentage errors of measurement in a, b, c and d are 1%, 3%,4% and 2% respectively. What is the percentage error in the quantity P? What is the value of P calculated using the above relation turns out to be 3.763, to value should you round off the result?
Q12. Name the technique used in locating.

(a) an under water obstacle

(b) position of an aeroplane in space.

Q13. Deduce dimensional formulae of—

(i) Boltzmann’s constant

(ii) mechanical equivalent of heat.

Q14. Give examples of dimensional constants and
dimensionless constants.