If the speed $v$ of transverse waves on a stretched string depends on the tension $T$ in the string and the mass per unit length $μ$ of the string, which of the following is dimensionally consistent?

Which does not have the same unit as others

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:

Which relation is wrong

A pressure of ${10^6}$ dyne ${\rm{c}}{{\rm{m}}^{ - 2}}$ is equivalent to

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

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

The SI unit of length is the metre. Suppose we adopt a new unit of length which equal x metre. The area of $1{m^2}$ expressed in terms of the new unit has a magnitude

A highly advanced alien civilization uses a unit of mass called a 'glorp' and a unit of length called a 'blarp'. Their fundamental unit of time is the 'zorp'. They discover a fundamental law of physics relating force (F), mass (m), length (l), and time (t) expressed as $F = K m^a l^b t^c$, where K is a dimensionless constant. If the dimensions of force in their system are glorp\cdot blarp \cdot zorp^{-2}$, what are the values of a, b, and c?

Precision in measurement depends on

Volt/metre is the unit of