Is `T=2pi sqrt(m/k)` Dimensionally correct?

Show that the expression of the time period T of a simple pendulum of length l given by T = 2pi sqrt((l)/(g)) is dimensionally currect

Equation s_t=u + at - 1/2 a does not seem dimensionally correct, why?

Test dimensionally if the formula t= 2 pi sqrt(m/(F/x)) may be corect where t is time period, F is force and x is distance.

With the usual notations , check if the following equation S_(t) = u + (1)/(2) a ( 2t -1) is dimensionally correct or not.

If T = 2pi sqrt(l/g) is the time period of a simple pendulu, then the unit of 4pi^(2) l/T^(2) in the SI system is ________ .

Using the dimensional analysis, check whether the following equation is correct or not: T=2pisqrt(R^(3)//GM) .

A body of mass m hung at one end of the spring executes simple harmonic motion . The force constant of a spring is k while its period of vibration is T . Prove by dimensional method that the equation T = 2 pi m // k is correct. Dervive the correct equation , assuming that they are related by a power law.

Consider the equation T = 2pi sqrt ((l)/(g)) and check whether it is correct or not.