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 unit of magnetic moment is

Which of the following units denotes the dimensions $\left[ {{\rm{M}}{{\rm{L}}^2}/{{\rm{Q}}^2}} \right],$, where Q denotes the electric charge?

Consider a new system of units in which c(speed of light in vacuum), h(Planck’s constant) and G(gravitational constant) are taken as fundamental units. Which of the following would correctly represent mass in this new system?

Unit of moment of inertia in MKS system

Which relation is wrong

Which of the following physical quantities has neither dimensions nor unit?

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 =

In the equation $F = ma$, if the unit of force ($F$) is newton (N), mass ($m$) is kilogram (kg), and acceleration ($a$) is $ms^{-2}$, is the equation dimensionally homogeneous?

A physical quantity is measured and its value is found to be nu where where n= numerical value and u= unit. Then which of the following relations is true

The SI unit of universal gas constant (R) is