The following pairs have same dimensional formula : (a) energy and torque (b) pressure and stress (c) b is correct (d) a and b are correct.
Answers
Answer:
dimensional formula of energy= [M L^2 T^-2]
dimensional formula of torque= [M L^2 T^-2]
dimensional formula of pressure=[M L^-1 T^-2]
dimensional formula of stress = [M L^-1 T^-2]
hence,
option a and b are correct.
We have to find the dimensional formulas of (a) Energy and Torque (b) Pressure and Stress and then find out which of the following pair has same dimensional formula.
(a) Energy = Mass × (Velocity)² [Velocity = Speed]
= Mass × (Distance × Time)²
= [M¹] [L¹T-¹]²
= [M¹] [L²T-²]
= [M¹L²T-²]
Torque = Force × Perpendicular distance
= (Mass × Acceleration) × Perpendicular distance
= (Mass × Velocity/Time) × Perpendicular distance
= [M¹L¹T-²] [L¹]
= [M¹L²T-²]
Therefore, dimensional formula of both Energy and Torque are same i.e. [M¹L²T-²]
(b) Pressure = Force/Area
= (Mass × Acceleration)/Area
= (Mass × Velocity/Time)/Area
= [M¹L¹T-²] [L²]-¹
= [M¹L-¹T-²]
Stress = Force/Area
= (Mass × Acceleration)/Area
= (Mass × Velocity/Time)/Area
= [M¹L¹T-²] [L²]-¹
= [M¹L-¹T-²]
(As Pressure = Stress)
Therefore, the dimensional formula of both Pressure and Stress are same i.e. [M¹L-¹T-²]
From above we can say that both (a) and (b) have same dimensional formula. So, correct answer is option (d) a and b are correct.