Question

if y represents pressure and x represents velocity gradient then the dimensions of d2y/dx2 are

1) ML-1T-2

2) M2L-2T-2

3) ML-1

4) M2L-2 T-4

Answer 1

y represents pressure and x represents velocity gradient
we know, pressure = force/area
∴ dimension of pressure = [MLT⁻²]/[L²]
∴ dimension of y = [ML⁻¹T⁻²]

Velocity gradient= dv/dx
∴dimension of velocity = [LT⁻¹]/[L]
∴ dimension of x = [T⁻¹]

here you should learn one thing ,
dimension of y = dimension of dy = dimension of d²y = dimension of dⁿy
But dimension of dx² = {dimension of x}²
dimension of dxⁿ = {dimension of x }ⁿ

Use above concept here,
then, dimension of d²y/dx² = {dimension of y}/{dimension of x}²
= [ML⁻¹T⁻²]/[T⁻¹]²
= [ML⁻¹T⁻²]/[T⁻²]
= [ML⁻¹]

Hence, option (3) is correct.

Answer 2

Answer: Here is the answer. Hope it helps.

The correct answer is option 3 [ML-1]

Explanation: