Its a numerical on dimensional analysis,please help

check the correctness of relation h=r p g/2 s where h is height,r radius ,p density, g acceleration due to gravity and s surface tension.write their dimensions in MLT and if found incorrect,deduce the correct form(needed an expert).

The equation you have written isn't clear. I'll assume you mean h=rpg/(2s) (i,e the denominator is 2s).

Use the symbol [x] to means 'the dimension of x'.

[h] = L

[r] = L

p = mass/volume so
[p] = M/L³ = ML⁻³

g = acceleration = velocity-change/time
[g] = (L/T)/T = L/T² = LT⁻²

2 is a pure number so is dimensionless - ignore it when using dimensional analysis.

s = force/distance = (mass x acceleration) / distance
[s] = M LT⁻² / L = MT⁻²
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Dimension of left side of equation = [h] = L

Dimension of right side of equation = [rpg/(2s)]
= L ML⁻³ LT⁻² / (MT⁻²)
= L⁻¹

So the left and right sides don't match and the equation is dimensionally incorrect
______________________________

The problem is that the power of L is wrong. M and T are OK. From inspection you can see that if r is replaced by r³, the dimensions would be
= L³ ML⁻³ LT⁻² / (MT⁻²)
= L
which matches the dimensions of h.

So the equation could be h=r³pg/(2s)

Note the factor 2 in the denominator may or may not be correct - dimensional analysis cannot tell you about the values of dimensionless constants in an equation.

steve is correct..