Measurements(Units, Dimensions & Errors)

1. The respective number of significant figure for numbers 0.007,6.032 and 2.64 x 10⁶
a)1,4,3
b)1,3,4
c)4,4,3
d)3,1,4

2)Charle's law PV=nRT is valid for ideal gases.Even for them, at extreme conditions such as high pressure, some crrections are needed.
The Van der Waal's equation of state for a mole of real gas, is given by

The dimensions of a and b are
a) ML²T^-2,L³
b) ML⁵T^-2,L⁶
c) ML⁵T^-2,L³
d) ML²T^-2,LT^-1

3) h/2π has the dimension of_______, where h is Planck's constant.
a) velocity
b) momentum
c) energy
d) angular momentum

4)The dimensions of 'resistance' are same as those of _______ where h is Planck's constant, e is the charge.
a)h²/e²
b)h²/e
c)h/e²
d)h/e

5) The position x of a particle at time t is given by:

where v₀ is a constant and a >0. The dimensions of v₀ and “a” are:

a)M⁰LT^-1,T^-1

b)M⁰LT⁰,T^-1

c)M⁰LT^-1,LT^-2

d)M⁰LT⁰,T

6)The number of particles(n) crossing a unit area perpendicular to x-axis in unit time is given by:

where, n₁,n₂ are the number of particles per unit volume at x=x₁ and x=x₂ respectively.
The dimensions of D called diffusion coefficient are:

a)L²T^-3
b)LT²
c)L²T^-2
d)L²T^-1


7)A soft iron rod has its length increased by 0.3% on increasing its temperature by ∆T. The percentage increase in the area of a circular hole in a sheet of the same material (soft iron) on increasing its temperature by ∆T will be
a) 0.3%
b) – 0.3%
c) -0.6%
d) 0.6%

8.Names of units of some physical quantities are given in List I and their dimensional formulae are
given in List II. Match the correct pairs in the lists

LIST I	LIST II
1) Pa s	(e) [L2T-2K-1]
2) Nm K–1	(f) [MLT–3K–1]
3) J kg–1K–1	(g)[ML–1T–11]
4) Wm–1K–1	(h)[ML–2T–2K–1]

      1     2     3    4
a)   h     g     e     f
b)   g     f      h    e
c)   g     e     h     f
d)   g     h     e     f



9.In planetary motion the areal velocity of position vector of a planet depends on angular velocity(ω) and the distance of the planet from sun (r). If so the correct relation for areal velocity is
a) dA/dt  ∝ rω
b) dA/dt  ∝ ω²r
c) dA/dt  ∝ ω r²
d) dA/dt  ∝ (ωr)^1/2


10.In C.G.S system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, meter and minute, the magnitude of the force is
a) 0.036
b) 0.36
c) 3.6
d) 36


                                                                                   Solutions will be published soon