Which of the following equations for kinetic energy K is RULED OUT by dimensional analysis? (K has dimensions [ML²T⁻²])
K = (3/16)mv²
K = \( \frac{1}{2} \)mv²
K = m²v³
Both A and B are ruled out
K = \( \frac{1}{2} \)mv² + ma is ruled out by dimensional analysis because:
\( \frac{1}{2} \) is not dimensionless
[\( \frac{1}{2} \)mv²] = [ML²T⁻²] and [ma] = [MLT⁻²] — two terms with DIFFERENT dimensions are added
v² has wrong dimensions for energy
m appears twice in the expression
Which of the following kinematic equations is dimensionally INCORRECT?
v = u + at
s = ut + \( \frac{1}{2} \)at²
v² = u + 2as
v² = u² + 2as
For T = 2π√(l/g), dimensional check of √(l/g) gives:
[L/LT⁻²]½ = [T²]½ = [T]
[L/LT⁻²]½ = [L²T⁻²]½ = [LT⁻¹]
[L/LT⁻²]½ = [T⁻²]½ = [T⁻¹]
[L/LT⁻²]½ = [L²]½ = [L]