The decay constant has dimensions of inverse time (T^-1), which is the same as frequency.

Dimensional homogeneity is used to check the correctness of equations; the OCR shows option C marked.

The OCR marks option B; incompressible fluids have constant density.

Tension, force and weight all have force dimensions, while modulus of elasticity has dimensions of pressure and is different.

980 cm s⁻² = 9.8 m s⁻²; converting to m hr⁻² multiply by (3600)² giving 9.8×12,960,000 ≈ 127,008,000 m hr⁻², so D is correct.

Work and torque both have dimensions of force × distance (N·m), so option A is correct.

Torque has units N·m = kg·m^2·s^-2, so its dimensional formula is M L^2 T^-2.

b/t must have dimensions of velocity (L T^-1), so b has dimensions L (i.e., M^0 L^1 T^0).

Dimensional analysis requires that the dimensions on both sides of a valid equation be the same.

G has dimension M^-1 L^3 T^-2; keeping metre and second unchanged, set new mass unit M' so 1 = G_SI*(1/M'), hence M' = G_SI = 6.67×10^-11 kg.