A physical quantity u is given by the relation $u = \frac{{{B^2}}}{{2{{\rm{\mu }}_0}}}$ here, B=magnetic field strength ${{\rm{\mu }}_0} =$ magnetic permeability of vacuum.

A calorie is a unit of heat and equal 4.2 J. Suppose we employ a system of units in which the unit of mass is $\alpha$ kg, the unit of length is $\beta$ metre and the unit of time is γ sec. In this new system. 1 calorie =

If the unit of force and length each be increased by four times, then the unit of energy is increased by

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree $\left( { = 0.5^\circ } \right),$ then the least count of the instrument is

SI unit of permittivity is

If $x = a + bt^2$, where $x$ is in meters and $t$ is in seconds, what are the dimensions of $b$?

Unit of stress is

Which of the following system of units is not based on units of mass, length and time alone

If the unit of length and force be increased four times, then the unit of energy is

The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}} + kx$, where $l$ is the length, $g$ is acceleration due to gravity, and $x$ is displacement. The dimensions of $k$ are:

The dimensions of calorie are