Check by the method of dimensions, whether the folllowing relation are dimensionally correct or not. (i) `upsilon = sqrt(P//rho)`, where `upsilon` is velocity. P is prerssure and `rho` is density. (ii) `v= 2pisqrt((I)/(g)),` where I is length, g is acceleration due to gravity and v is frequency.

Check the dimensional consistency of the relation upsilon = (1)/(I) sqrt((P)/(rho)) where I is length, upsilon is velocity, P is pressure and rho is density,

The dimensions of gamma in the relation v = sqrt((gamma p)/(rho)) (where v is velocity, p is pressure , rho is density)

Check by the method of dimensions whether the following relations are true. (i) t=2pisqrt(l/g) , (ii) v=sqrt(P/D) where v= velocity of sound P=pressure D=density of medium . (iii) n=1/(2l)=sqrt(F/m) where n= frequency of vibration l=length of the string, F=stretching force m=mass per unit length of the string .

Find the dimensions of K in the relation T = 2pi sqrt((KI^2g)/(mG)) where T is time period, I is length, m is mass, g is acceleration due to gravity and G is gravitational constant.

Check the correctness of the relation T=2pisqrt((l)/(g)) , where T is the time period, l is the length of pendulum and g is acceleration due to gravity.

According to Bernoulli's theorem (p)/(d) + (v^(2))/(2) + gh = constant is ( P is pressure, d is density, h is height, v is velocity and g is acceleration due to gravity)

Obtain dimension of rho gv where, rho = density, g = acceleration, v = velocity

Test if the following equation is dimensionally correct: h= ((sS cos theta)/(r p g)) where h= height, S= surface tension, p= density, r=radius, and g= acceleration due to gravity.

If V = sqrt(gammap)/(rho) , then the dimensions of gamma will be (where p is pressure, rho is density and V is velocity) :