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The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2
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The position of a particle at time 't' is given by the relationx(t) = ...
**Answer:**
The given relation for the position of a particle at time 't' is x(t) = V0t + (1/2)at^2.
**Dimensions of V0 and a:**
The dimensions of a physical quantity represent its fundamental units of measurement. In the given relation, V0 and a both have different dimensions. Let's calculate the dimensions of V0 and a using the dimension formulae:
- Dimension of distance (x) = [L]
- Dimension of time (t) = [T]
**Dimension of V0:**
We know that the dimension of displacement (x) is [L]. Therefore, the dimension of V0t must be [L].
- Dimension of V0t = [L]
- Dimension of time (t) = [T]
By the formula of dimension, we have:
[M^0L^1T^0] = V0 [M^0L^1T^0]
Simplifying this equation, we get:
- Dimension of V0 = [M^0L^1T^0]
Therefore, the dimension of V0 is M^0L^1T^0.
**Dimension of a:**
We know that the dimension of distance (x) is [L]. Therefore, the dimension of (1/2)at^2 must be [L].
- Dimension of (1/2)at^2 = [L]
- Dimension of time (t) = [T]
By the formula of dimension, we have:
[M^0L^1T^0] = a [M^0L^1T^-2]
Simplifying this equation, we get:
- Dimension of a = [M^0L^1T^-2]
Therefore, the dimension of a is M^0L^1T^-2.
**Conclusion:**
The dimensions of V0 and a are M^0L^1T^0 and M^0L^1T^-2 respectively.
The given relation for the position of a particle at time 't' is x(t) = V0t + (1/2)at^2.
**Dimensions of V0 and a:**
The dimensions of a physical quantity represent its fundamental units of measurement. In the given relation, V0 and a both have different dimensions. Let's calculate the dimensions of V0 and a using the dimension formulae:
- Dimension of distance (x) = [L]
- Dimension of time (t) = [T]
**Dimension of V0:**
We know that the dimension of displacement (x) is [L]. Therefore, the dimension of V0t must be [L].
- Dimension of V0t = [L]
- Dimension of time (t) = [T]
By the formula of dimension, we have:
[M^0L^1T^0] = V0 [M^0L^1T^0]
Simplifying this equation, we get:
- Dimension of V0 = [M^0L^1T^0]
Therefore, the dimension of V0 is M^0L^1T^0.
**Dimension of a:**
We know that the dimension of distance (x) is [L]. Therefore, the dimension of (1/2)at^2 must be [L].
- Dimension of (1/2)at^2 = [L]
- Dimension of time (t) = [T]
By the formula of dimension, we have:
[M^0L^1T^0] = a [M^0L^1T^-2]
Simplifying this equation, we get:
- Dimension of a = [M^0L^1T^-2]
Therefore, the dimension of a is M^0L^1T^-2.
**Conclusion:**
The dimensions of V0 and a are M^0L^1T^0 and M^0L^1T^-2 respectively.
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The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2
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The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2 for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2 covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2.
The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2 for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2 covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position of a particle at time 't' is given by the relationx(t) = where V0 is a constant and a > 0. The dimensions of V0 and a are respectively.A :M0L1T0 and T_1B :M0L1T0 and T_2C :M0L1T_1 and T_1D :M0L1T_1 and T_2.
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