.The velocity of a particle moving along the X-axis is given by v = p + qt3 – rt4. where t is the time. Find the dimensions of the constants p, q and r.
Answers
Given :-
v = p + qt³ - rt⁴
We will take single terms and compare with the dimension of velocity i.e. L/T.
v = p = L/T
[P] = L/T.
Now, Taking second term.
qt³ = L/T
[Q] = L/T⁴.
Again, For third term.
rt⁴ = L/T
[R] = L/T⁵
Hence,
The dimension of constant are as follow :-
[P] = L/T
[Q] = L/T⁴
[R] = L/T⁵
Some other dimensions which are necessary.
1. Density = D = [ML-³T⁰]
2. Acceleration = a = [M⁰LT-²]
3. Energy = [ML²T-²]
4. Strain = [M⁰L⁰T⁰] = No units.
5. Plank's Constant = [ML²T-¹]
6. Electric Intensity = [MLT-³A-¹]
7. Electric Potential = [ML²T-³A-¹]
8. Moment of Inertia = [ML²T⁰]
9. Surface Tension = [ML⁰T-²]
10. Frequency = [M⁰L⁰T-¹]
Answer:
Explanation:
v = p + qt³ - rt⁴
We will take single terms and compare with the dimension of velocity i.e. L/T.
v = p = L/T
[P] = L/T.
Now, Taking second term.
qt³ = L/T
[Q] = L/T⁴.
Again, For third term.
rt⁴ = L/T
[R] = L/T⁵
Hence,
The dimension of constant are as follow :-
[P] = L/T
[Q] = L/T⁴
[R] = L/T⁵
Some other dimensions which are necessary.
1. Density = D = [ML-³T⁰]
2. Acceleration = a = [M⁰LT-²]
3. Energy = [ML²T-²]
4. Strain = [M⁰L⁰T⁰] = No units.
5. Plank's Constant = [ML²T-¹]
6. Electric Intensity = [MLT-³A-¹]
7. Electric Potential = [ML²T-³A-¹]
8. Moment of Inertia = [ML²T⁰]
9. Surface Tension = [ML⁰T-²]
10. Frequency = [M⁰L⁰T-¹]