Units And Measurement

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Dimensions of resistance in an electrical circuit, in terms of the dimension of mass M, of length L, of time T and of current I, would be:

[ML²T^-3I^-1]

[ML²T^-2]

[ML²T^-1I^-1]

[ML²T^-3I^-2]

Solution

[ML²T^-3I^-2]

Resistance
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If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

[Ev^-2T^-1]

[Ev^-1T^-2]

[Ev^-2T^-2]

[E^-2v^-1T^-3]

Solution

[Ev^-2T^-2]

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If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are

[FvT^-1]

[FvT^-2]

[Fv^-1T^-1]

[Fv^-1T]

Solution

[Fv^-1T]

We know that,
F = ma
That is,
F = mv/t
$straight m space equals space Ft over straight v$
So, $left square bracket straight M right square bracket space equals space fraction numerator left square bracket straight F right square bracket left square bracket straight T right square bracket over denominator left square bracket straight V right square bracket end fraction space equals space left square bracket space Fv to the power of negative 1 end exponent straight T right square bracket$

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If the dimensions of a physical quantity are given by M^a L^b T^c, the physical quantity will be

pressure if a = 1, b = -1, c= 2

velocity if a = 1, b = 1, c = -2

acceleration if a = 1, b = 1, c =-2

force if a = 0, b = -1, c =- 2

Solution

pressure if a = 1, b = -1, c= 2

Dimensions of velocity = [ M⁰L¹T^-1]
Here, a = 0, b =1, c = -1
Dimension of acceleration = [ M⁰L¹T^-2]
Dimension of force = [ M¹L¹T^-2]
Dimension of pressure = [M¹L^-1T^-2
The physical quantity is pressure.

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If the error in the measurement of radius of sphere is 2%, then the error in the determination of volume of the sphere will be

4%

6%

8%

2%

Solution

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Units And Measurement

Dimensions of resistance in an electrical circuit, in terms of the dimension of mass M, of length L, of time T and of current I, would be:

[ML²T^-3I^-1]

[ML²T^-2]

[ML²T^-1I^-1]

[ML²T^-3I^-2]

If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

[Ev^-2T^-1]

[Ev^-1T^-2]

[Ev^-2T^-2]

[E^-2v^-1T^-3]

If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are

[FvT^-1]

[FvT^-2]

[Fv^-1T^-1]

[Fv^-1T]

If the dimensions of a physical quantity are given by M^a L^b T^c, the physical quantity will be

pressure if a = 1, b = -1, c= 2

velocity if a = 1, b = 1, c = -2

acceleration if a = 1, b = 1, c =-2

force if a = 0, b = -1, c =- 2

If the error in the measurement of radius of sphere is 2%, then the error in the determination of volume of the sphere will be

4%

6%

8%

2%

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Units And Measurement

Dimensions of resistance in an electrical circuit, in terms of the dimension of mass M, of length L, of time T and of current I, would be: [ML2T-3I-1] [ML2T-2] [ML2T-1I-1] [ML2T-3I-2]

If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be [Ev-2T-1] [Ev-1T-2] [Ev-2T-2] [E-2v-1T-3]

If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are [FvT-1] [FvT-2] [Fv-1T-1] [Fv-1T]

If the dimensions of a physical quantity are given by Ma Lb Tc, the physical quantity will be pressure if a = 1, b = -1, c= 2 velocity if a = 1, b = 1, c = -2 acceleration if a = 1, b = 1, c =-2 force if a = 0, b = -1, c =- 2

If the error in the measurement of radius of sphere is 2%, then the error in the determination of volume of the sphere will be 4% 6% 8% 2%

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Dimensions of resistance in an electrical circuit, in terms of the dimension of mass M, of length L, of time T and of current I, would be:

[ML²T^-3I^-1]

[ML²T^-2]

[ML²T^-1I^-1]

[ML²T^-3I^-2]

If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

[Ev^-2T^-1]

[Ev^-1T^-2]

[Ev^-2T^-2]

[E^-2v^-1T^-3]

If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are

[FvT^-1]

[FvT^-2]

[Fv^-1T^-1]

[Fv^-1T]

If the dimensions of a physical quantity are given by M^a L^b T^c, the physical quantity will be

pressure if a = 1, b = -1, c= 2

velocity if a = 1, b = 1, c = -2

acceleration if a = 1, b = 1, c =-2

force if a = 0, b = -1, c =- 2

If the error in the measurement of radius of sphere is 2%, then the error in the determination of volume of the sphere will be

4%

6%

8%

2%