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WorksheetsPhysical World And Measurement
Total questions: 41
Worksheet time: 41mins
A Physical quantity of the dimensions of length that can be formed out of c, G and e2 ⁄ 4πEo is [ c is velocity of light,G is universal constant of gravitation and e is charge ]
1/c2 [ G e2/4πE0 ]1/2
c2 [ G e2/4πE0 ]1/2
1/c2 [ e2/ G 4πE0 ]1/2
1/c G e2 / 4πE0
If enegry (E),velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
[Ev-2T-1]
[Ev-1T-2]
[Ev-2T-2]
[Ev-2 v-1 T-3]
if dimension of critical velocity vc of a liquid flowing through a tube are expressed as [nx py rz], where n p and r are the coefficient of viscosity of liquid density of liquid and radius of the tube respectively, then the values of x, y and z are given by
1,-1,-1
-1,-1,1
-1,-1,-1
1,1,1
If force (F),velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are
[FvT-1]
[FvT-2]
[Fv-1T-1]
[Fv-1T]
In an experiment,four quantities a,b,c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated P= a3b2/cd %. Error in P is
14%
10%
7%
4%
The dimensions of (μ0ε0)-½ are
[ L½ T-½ ]
[ L-1T ]
[ L T-1 ]
[ L½ T½ ]
The dimension of ½ ε0E, Where ε0 is permittitvity of free space and E is electric field are
[ML2 T-2]
[ML-1 T-2]
[ML2 T-1]
[MLT-1]
If the dimensions of a physical quantity are given by [MaLb Tc], then the physical quantity will be
pressure if a =1, b = -1, c = - 2
velocity if a = 1, b = 0, c = - 2
acceleration if a =1, b = 1, c = -2
force if a = 0, b = -1, c = -2
which two of the following five physical parameters have the same dimensions ?
(i) Energy Density (ii) Refractive index (iii) Dielectric constant (iv) Young's modulus (v) Magnetic field
(i) and (iv)
(iii) and (v)
(i) and (iv)
(i) and (v)
If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
4%
6%
8%
2%
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
[ML2 T-3I-1 ]
[ML2 T-2 ]
[ML2 T-1I-1 ]
[ML2 T-3I-2 ]
The Velocity v of a particle at time t is given by v = at+ b/t+c, where a,b,and c are constants. The dimensions of a,b, and c are respectively
[LT-2]. [L] and [T]
[L2]. [T] and [LT2]
[LT2],[LT] and [L]
[L],[LT] and [LT2]
The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimension of
frequency
velocity
angular momentum
time
The dimensions of universal gravitational constant are
[M-1L3 T-2]
[ML2 T-1]
[M-2L3 T-2]
[M-2L2 T-1]
The unit of permittivity of free space,E0 is
coulomb/newton - metre
newton - metre2/coulomb2
coulomb2/newton - metre2
coulomb2/(newton - metre2)
The value of Planck's constant in SI unit is
6.63 × 10-31 J-s
6.63 × 10-30 kg-m/s
6.63 × 10-32 kg-m2
6.63 × 10-34 J-s
Planck's constant has the dimensions of
linear momentum
angular momentum
enegry
power
A pair of physical quantities having same dimensional formula is
force and torque
work and enegry
force and impulse
linear momentum and angular momentum
The dimensional formula for magnetic flux is
[ML2T-2 A-1]
[ML3T-2 A-2]
[M0L2T-2 A-2]
[ML2T-1 A2]
The force f on a sphere of radius r moving in a medium with velocity ν is given by F = 6πηrν
[ML-3]
[MLT-2]
[MT-1]
[ML-1 T -1]
Which of the following will have the dimensions of time ?
LC
R/L
L/R
C/L
The Density of a cube is measured by measuring its mass and length of its sides if the maximum error in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of density will be
7%
9%
12%
13%
An equation is given [p+a/v2] = b θ/v
where p = pressure, V = volume and θ = absolute temperature. if a and b are constants, then the dimensions of a will be
[ML5T-2]
[M-1 L5 T2]
[ML-5T-1]
[ML5T]
The Percentage errors in the measurement of mass and speed are 2% and 3% respectively, The error in kinetic energy obtained by measuring mass and speed will be
12%
10%
8%
2%
Which of the following is a dimensional constant?
Refractive index
Poisson's ratio
Relative density
Gravitational constant
In a vernier callipers N divisions of vernier scale coincide with N -1 divisions of main scale ( in which length of one division is 1mm). The least count of the instrument should be
N
N-1
1/10N
1/(N -1)
In a particular system, the unit of length mass and time are chosen to be 10cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to
0.1 N
1 N
10 N
100 N
Turpentine oil is flowing through a tube of length Ι and radius r. The pressure difference between the two ends of the tube is p. The Viscosity of oil is given by
η = Ρ(r2 - x2) / 4vΙ
Where,v is the velocity of oil at distance x from the axis of the tube.The dimensions of η are
[M0L0T0]
[MLT-1]
[ML2T-2]
[ML-1T-1]
The time dependence of physical quantity p is given by p = p0 exp (-αt2), where α is a constant and t is the time. The constant α
is dimensionless
has dimensions [T-2]
has dimensions [T2]
has dimensions of ρ
If ρ represents radiation pressure, c represents speed of light and S represents radiation energy striking until area per sec. The non -zero integers x,y,z such that Px Sy Cz is dimensionless are
x = 1, y =1, z = 1
x = -1, y =1, z = 1
x = 1, y = -1, z = 1
x = 1, y =1, z = -1
The Dimensional formula for permeability of free space, μ0 is
[MLT-2A-2]
[ML-1T1A-2]
[ML-1T-2A2]
[MLT-2A-1]
A Certain body weighs 22.42 g and has a measured volume of 4.7cc, The possible error in the measurement of mass and volume are 0.01g and 0.1 cc. Then maximum error in the density will be
22%
0.2%
2%
0.02%
The frequency of vibration ∱ = Cm x k y, Where C is a dimensionless constant. The values of x and y are
x = 1/2,y= 1/2
x = -1/2,y= -1/2
x = 1/2,y= -1/2
x = -1/2,y= 1/2
According to Newton, the viscous force acting between liquid layers of area A and velocity gradient Δν/Δz is given by F = -ηΑ dν/dz, where η is constant called
[ML-2lT-2]
[M0L0T0]
[ML2T-2]
[ML-1T-1]
The dimensional formula of pressure is
[MLT-2]
[ML-1T2]
[ML-1T-2]
[ML-1T-1]
The dimensional formula of torque is
[ML2T-2]
[MLT-2]
[ML-1T-2]
[ML-2T-2]
If x = αt +bt2 , where x is the distance travelled by the body in kilometer while t is the time in second, then the unit of b is
km/s
km-s
km/s2
km-s2
Dimensional formula of self - inductance is
[MLT-2 A-2]
[ML2T-1A-2]
[ML2T-2 A-2]
[ML2T-2A-1]
Of the following quantities, which one has dimensions different from the remaining three?
Energy per unit volume
Force per unit area
Product of voltage and charge per unit volume
Angular momentum
The dimensional formual for angular
[M0L2T-2]
[ML2T-1]
[MLT-1]
[ML2T-2]
If C and R denote capacitance and resistance respectively, then the dimensional formula of CR is
[M0L0T]
[M0L0T0]
[M0L0T-1]
Not expressible i terms of [MLT]
