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

If the force is proportional to square of velocity, then the dimension of proportionality constant is

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

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

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?

Round off the following numbers as indicated 101.55 \(\times\) 10⁶ up to 4 digits

Round off the following numbers as indicated 248337 up to digits 3 digits

Round off the following numbers as indicated 12.653 up to 3 digits.

The initial and final temperatures of a liquid in a container are observed to be 75.4 ± 0.5°C and 56.8 ± 0.2°C. Find the fall in the temperature of the liquid.

The voltage across a wire is (100 ± 5)V and the current passing through it is (10 ± 0.2) A. Find the resistance of the wire.

Arrive at Einstein's mass-energy relation by dimensional method (E = mc²).

The shadow of a pole standing on a level ground is found to be 45 m longer when the sun's altitude is 30^o than when it was 60^o. Determine the height of the pole. [Given \(\sqrt { 3 } \)=1.73]

Explain the principle of homogeniety of dimensions. What are its uses? Give example