Physical World, Units & Measurements

What is the fractional error in g calculated from T = 2π √l/ g? Given fraction errors in T and l are ± x and ± y respectively?

The dimensional formula of the constant a in Vander Waal’s gas equation
(P+^a⁄_V²)(V-b)=RT is

Young’s modulus of a material has the same unit as that of

The dimensions of Reynold’s constant are

If the error in the measurement of the volume of sphere is 6%, then the error in the measurement of its surface area will be

If the capacitance of a nanocapacitor is measured in terms of a unit ‘u‘ made by combining the electric charge ‘e‘, Bohr radius ‘a_o‘, Planck’s constant ‘h‘ and speed of light ‘c‘ then

Dimensions of coefficient of viscosity is

The dimensions of mobility are

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimensions of constant of proportionality are

The Richardson equation is given by I=AT²e^—B/kT. The dimensional formula for AB² is same as that for

The dimensional formula of farad is

Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimensional formula of permittivity is

The siemen is the SI unit of

Weber is the unit of

The dimensional formula for magnetic flux is

Of the following quantities, which one has dimensions different from the remaining three?

The dimensions of Planck’s constant are

Which of the following pairs does not have similar dimensions?

If e is the charge, V the potential difference, T the temperature, then the units of eV /T are the same as that of

A quantity X is given by ε_oL ^ΔV⁄_Δt where ε_o is the permittivity of the free space, L is a length, ΔV is a potential difference and Δt is a time interval. The dimensional formula for X is the same as that of

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be:

If velocity (V), force (F) and energy (E) are taken as fundamental units, then dimensional formula for mass will be

If E, m, J and G represent energy, mass, angular momentum and gravitational constant respectively, then the dimensional formula of EJ²/m⁵G² is same as that of the

The pressure on a square plate is measured by measuring the force on the plate and length of the sides of the plate by using the formula P = F/l². If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is

The time period of a body under S.H.M. is represented by:
T = P^a D^b S^c where P is pressure, D is density and S is surface tension, then values of a, b and c are

The dimensions of energy are

What is the dimensions of impedance?

If Q denote the charge on the plate of a capacitor of capacitance C then the dimensional formula for Q²/C is

Which two of the following five physical parameters have the same dimensions?

(A) Energy density           (B) Refractive index

(C) Dielectric constant    (D) Young’s modulus

(E) Magnetic field

The physical quantities not having same dimensions are

The dimensions of ¹⁄₂ ε₀E² ( ε₀ : permittivity of free space, E electric field) are

The dimensional formula for torque is

The density of material in CGS system of units is 4g/cm³. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be

Which of the following pair of quantities do not have the same dimensions

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

The unit of impulse is the same as that of

Two quantities A and B have different dimensions which mathematical operation given below is physically meaningful?

Which is different from others by units?

Velocity of light is equal to

The dimensions of Wien’s constant are

The velocity of water waves (v) may depend on their wavelength l, the density of water r and the acceleration due to gravity, g. The method of dimensions gives the relation between these quantities is

What is the dimensional formula of gravitational constant?

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10^-3 are

The physical quantity which has the dimensional formula [M¹T^-3] is

The speed of light (c), gravitational constant (G) and planck’s constant (h) are taken as fundamental units in a system. The dimensions of time in this new system should be