lower six- chapter 1 练习

LOWER SIX


1. What is the dimension of the following?
i) velocity
[v] = [s] / [t]
= L T-¹
ii) kg m² s-²
[kg m² s-²] = M L² T-²


2. What is the dimension and SI unit for the following quantities?
i) Area
[A] = L x L
= L²
SI unit :
ii) Density
[ρ ] = [m / V]
= ML-³
SI unit : kg m-³
iii) Displacement
[s] = L
SI unit : m
iv) volume
[V] = L³
SI unit : m³
v) acceleration
[a] = LT-²
SI unit : m s-²

3. Determine whether the following is homogenous
i) s=vt, where s,v,t are distance , velocity and time
[s] = L
[vt] = LT-¹ • T
= T
∴ [s] = [vt] , the equation is homogenous
ii) c²= F/m , where c is the velocity of the wave which transverse a wire of F tension and mass m
[c²] = (LT-¹)²
= L²T-²

4. The velocity of sound (v) in an elastic medium depends on the density of the medium and a constant E as shown in the following equation :
v= E^(½) ρ^(-½)
E = v² ρ
[E] = L² T-² • M L-³
= M L-¹ T-²
SI unit : kg m-¹ s-²