Which of the following pairs of physical quantities have same dimension?

(a)

force and power

(b)

torque and energy

(c)

torque and power

(d)

force and torque

The velocity of a particle v at an instant t is given by v = at + br². The dimensions of b is

(a)

[L]

(b)

[LT^-1]

(c)

[LT^-2]

(d)

[LT^-3]

The density of a material in CGS system of units is 4 g cm^-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

(a)

0.04

(b)

0.4

(c)

40

(d)

400

The dimension of \({\left( {\mu}_{0}{\epsilon}_{0} \right)}^{{{1}\over{2}}}\) is

(a)

length

(b)

time

(c)

velocity

(d)

force

A length-scale (I) depends on the permittivity (e) of a dielectric material,  Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression for I is dimensionally correct?

(a)

\(l=\sqrt{{{nq^2}\over{\epsilon {k}_{B}T}}}\)

(b)

\(l=\sqrt{{{\epsilon {k}_{B}T}\over{nq^2}}}\)

(c)

\(l=\sqrt{{{q^2}\over{e{n}^{{{2}\over{3}}}{k}_{B}}T}}\)

(d)

\(l=\sqrt{{{q^2}\over{\epsilon n{k}_{B}T}}}\)