RRB Technician Grade 1 Model Paper 1

Concept:Dimensional formula of two quantities is same only when they have identical powers of mass, length, and time.Explanation:Let us check each pair by writing their dimensional formulas.1. Work $=$ Force $\times$ Displacement $= [MLT^{-2}] \times [L] = [ML^{2}T^{-2}]$Torque $=$ Force $\times$ perpendicular distance $= [MLT^{-2}] \times [L] = [ML^{2}T^{-2}]$So, Work and Torque have the same dimensions.2. Angular momentum $= mvr = [M] \times [LT^{-1}] \times [L] = [ML^{2}T^{-1}]$Planck's constant, $h = \frac{E}{\nu} = \frac{[ML^{2}T^{-2}]}{[T^{-1}]} = [ML^{2}T^{-1}]$So, Angular momentum and Planck's constant have the same dimensions.3. Tension is a force, so its dimension is $[MLT^{-2}]$Surface tension $= \frac{\text{Force}}{\text{length}} = \frac{[MLT^{-2}]}{[L]} = [MT^{-2}]$Hence, Tension and Surface tension do not have the same dimensional formula.4. Impulse $=$ Force $\times$ time $= [MLT^{-2}] \times [T] = [MLT^{-1}]$Linear momentum $=$ mass $\times$ velocity $= [M] \times [LT^{-1}] = [MLT^{-1}]$So, Impulse and Linear momentum have the same dimensions.Thus, only pair C has different dimensional formulas.Answer:Option C — Tension and Surface tension.