367345
Consider the following equation of Bernoulli's theorem \(p+\dfrac{1}{2} \rho v^{2}+\rho g h=k(\) constant \()\). The dimensions of \(k / p\) are same as that of which of the following?
1 Thrust
2 Pressure
3 Angle
4 Viscosity
Explanation:
The given equation of Bernoulli's theorem is \(=p+\dfrac{1}{2} \rho v^{2}+\rho g h=k\) where, \(p\) is pressure, \(\rho\) is density, \(g\) is acceleration due to gravity and \(h\) is height. We know that, every equation relating physical quantities should be in dimensional balance. It means dimensions of terms on both sides must be same. Hence, \(k\) has same dimensions as \(p\) and so \(\dfrac{k}{p}\) is dimensionless. Out of the given four options, angle is a dimensionless quantity.
PHXI02:UNITS AND MEASUREMENTS
367346
Dimensions are not same for the pair
1 Torque and work
2 Momentum and impulse
3 Pressure and stress
4 Power and strain
Explanation:
\({[P]=\left[{ML}^{-1} {~T}^{-3}\right]}\) But strain is dimensionless. So correct option is (4)
PHXI02:UNITS AND MEASUREMENTS
367347
The dimension of mass is zero in the following physical quantities.
1 Surface tension
2 Coefficient of viscosity
3 Heat
4 Specific heat capacity
Explanation:
Conceptual Question
PHXI02:UNITS AND MEASUREMENTS
367348
Which one of the following is NOT correct?
1 Dimensional formula of thermal conductivity (\(K\)) is \({M^1}{L^1}{T^{ - 3}}{K^{ - 1}}\)
2 Dimensional formula of potential (\(V\)) is \({M^1}{L^2}{T^3}{A^{ - 1}}\)
3 Dimensional formula of permeability of free space \(({\mu _0})\) is \({M^1}{L^2}{T^{ - 2}}{A^{ - 2}}\)
4 Dimensional formula of \(RC\) is \({M^0}{L^0}{T^{ - 1}}\)
Explanation:
Thermal conductivity \({\text{ = }}\frac{{{\text{Heat}}\;{\text{energy}}\; \times \;{\text{thickness}}}}{{{\text{Area}}\; \times \;{\text{Temperature}}\; \times \;{\text{time}}}}\) \([K] = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ {{L^2}} \right]\left[ K \right]\left[ T \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 3}}{K^{ - 1}}} \right]\) Potential \( = \frac{{Work}}{{Charge}}\) \([V] = \frac{{M{L^2}{T^{ - 2}}}}{{\left[ {AT} \right]}}\; = \;\left[ {{M^1}{L^2}{T^{ - 3}}{A^{ - 1}}} \right]\) Permeability of free space \({\text{ = }}\frac{{{\text{force}}\; \times \;{\text{distance}}}}{{{\text{current}}\; \times \;{\text{current}}\; \times \;{\text{length}}}}\) \(\left[ {{\mu _0}} \right]\; = \;\frac{{\left[ {ML{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ A \right]\left[ A \right]\left[ L \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}} \right]\) \(RC\) is the time constant of \(RC\) circuit. \([RC] = [{M^0}{L^0}{T^1}]\)
367345
Consider the following equation of Bernoulli's theorem \(p+\dfrac{1}{2} \rho v^{2}+\rho g h=k(\) constant \()\). The dimensions of \(k / p\) are same as that of which of the following?
1 Thrust
2 Pressure
3 Angle
4 Viscosity
Explanation:
The given equation of Bernoulli's theorem is \(=p+\dfrac{1}{2} \rho v^{2}+\rho g h=k\) where, \(p\) is pressure, \(\rho\) is density, \(g\) is acceleration due to gravity and \(h\) is height. We know that, every equation relating physical quantities should be in dimensional balance. It means dimensions of terms on both sides must be same. Hence, \(k\) has same dimensions as \(p\) and so \(\dfrac{k}{p}\) is dimensionless. Out of the given four options, angle is a dimensionless quantity.
PHXI02:UNITS AND MEASUREMENTS
367346
Dimensions are not same for the pair
1 Torque and work
2 Momentum and impulse
3 Pressure and stress
4 Power and strain
Explanation:
\({[P]=\left[{ML}^{-1} {~T}^{-3}\right]}\) But strain is dimensionless. So correct option is (4)
PHXI02:UNITS AND MEASUREMENTS
367347
The dimension of mass is zero in the following physical quantities.
1 Surface tension
2 Coefficient of viscosity
3 Heat
4 Specific heat capacity
Explanation:
Conceptual Question
PHXI02:UNITS AND MEASUREMENTS
367348
Which one of the following is NOT correct?
1 Dimensional formula of thermal conductivity (\(K\)) is \({M^1}{L^1}{T^{ - 3}}{K^{ - 1}}\)
2 Dimensional formula of potential (\(V\)) is \({M^1}{L^2}{T^3}{A^{ - 1}}\)
3 Dimensional formula of permeability of free space \(({\mu _0})\) is \({M^1}{L^2}{T^{ - 2}}{A^{ - 2}}\)
4 Dimensional formula of \(RC\) is \({M^0}{L^0}{T^{ - 1}}\)
Explanation:
Thermal conductivity \({\text{ = }}\frac{{{\text{Heat}}\;{\text{energy}}\; \times \;{\text{thickness}}}}{{{\text{Area}}\; \times \;{\text{Temperature}}\; \times \;{\text{time}}}}\) \([K] = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ {{L^2}} \right]\left[ K \right]\left[ T \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 3}}{K^{ - 1}}} \right]\) Potential \( = \frac{{Work}}{{Charge}}\) \([V] = \frac{{M{L^2}{T^{ - 2}}}}{{\left[ {AT} \right]}}\; = \;\left[ {{M^1}{L^2}{T^{ - 3}}{A^{ - 1}}} \right]\) Permeability of free space \({\text{ = }}\frac{{{\text{force}}\; \times \;{\text{distance}}}}{{{\text{current}}\; \times \;{\text{current}}\; \times \;{\text{length}}}}\) \(\left[ {{\mu _0}} \right]\; = \;\frac{{\left[ {ML{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ A \right]\left[ A \right]\left[ L \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}} \right]\) \(RC\) is the time constant of \(RC\) circuit. \([RC] = [{M^0}{L^0}{T^1}]\)
367345
Consider the following equation of Bernoulli's theorem \(p+\dfrac{1}{2} \rho v^{2}+\rho g h=k(\) constant \()\). The dimensions of \(k / p\) are same as that of which of the following?
1 Thrust
2 Pressure
3 Angle
4 Viscosity
Explanation:
The given equation of Bernoulli's theorem is \(=p+\dfrac{1}{2} \rho v^{2}+\rho g h=k\) where, \(p\) is pressure, \(\rho\) is density, \(g\) is acceleration due to gravity and \(h\) is height. We know that, every equation relating physical quantities should be in dimensional balance. It means dimensions of terms on both sides must be same. Hence, \(k\) has same dimensions as \(p\) and so \(\dfrac{k}{p}\) is dimensionless. Out of the given four options, angle is a dimensionless quantity.
PHXI02:UNITS AND MEASUREMENTS
367346
Dimensions are not same for the pair
1 Torque and work
2 Momentum and impulse
3 Pressure and stress
4 Power and strain
Explanation:
\({[P]=\left[{ML}^{-1} {~T}^{-3}\right]}\) But strain is dimensionless. So correct option is (4)
PHXI02:UNITS AND MEASUREMENTS
367347
The dimension of mass is zero in the following physical quantities.
1 Surface tension
2 Coefficient of viscosity
3 Heat
4 Specific heat capacity
Explanation:
Conceptual Question
PHXI02:UNITS AND MEASUREMENTS
367348
Which one of the following is NOT correct?
1 Dimensional formula of thermal conductivity (\(K\)) is \({M^1}{L^1}{T^{ - 3}}{K^{ - 1}}\)
2 Dimensional formula of potential (\(V\)) is \({M^1}{L^2}{T^3}{A^{ - 1}}\)
3 Dimensional formula of permeability of free space \(({\mu _0})\) is \({M^1}{L^2}{T^{ - 2}}{A^{ - 2}}\)
4 Dimensional formula of \(RC\) is \({M^0}{L^0}{T^{ - 1}}\)
Explanation:
Thermal conductivity \({\text{ = }}\frac{{{\text{Heat}}\;{\text{energy}}\; \times \;{\text{thickness}}}}{{{\text{Area}}\; \times \;{\text{Temperature}}\; \times \;{\text{time}}}}\) \([K] = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ {{L^2}} \right]\left[ K \right]\left[ T \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 3}}{K^{ - 1}}} \right]\) Potential \( = \frac{{Work}}{{Charge}}\) \([V] = \frac{{M{L^2}{T^{ - 2}}}}{{\left[ {AT} \right]}}\; = \;\left[ {{M^1}{L^2}{T^{ - 3}}{A^{ - 1}}} \right]\) Permeability of free space \({\text{ = }}\frac{{{\text{force}}\; \times \;{\text{distance}}}}{{{\text{current}}\; \times \;{\text{current}}\; \times \;{\text{length}}}}\) \(\left[ {{\mu _0}} \right]\; = \;\frac{{\left[ {ML{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ A \right]\left[ A \right]\left[ L \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}} \right]\) \(RC\) is the time constant of \(RC\) circuit. \([RC] = [{M^0}{L^0}{T^1}]\)
367345
Consider the following equation of Bernoulli's theorem \(p+\dfrac{1}{2} \rho v^{2}+\rho g h=k(\) constant \()\). The dimensions of \(k / p\) are same as that of which of the following?
1 Thrust
2 Pressure
3 Angle
4 Viscosity
Explanation:
The given equation of Bernoulli's theorem is \(=p+\dfrac{1}{2} \rho v^{2}+\rho g h=k\) where, \(p\) is pressure, \(\rho\) is density, \(g\) is acceleration due to gravity and \(h\) is height. We know that, every equation relating physical quantities should be in dimensional balance. It means dimensions of terms on both sides must be same. Hence, \(k\) has same dimensions as \(p\) and so \(\dfrac{k}{p}\) is dimensionless. Out of the given four options, angle is a dimensionless quantity.
PHXI02:UNITS AND MEASUREMENTS
367346
Dimensions are not same for the pair
1 Torque and work
2 Momentum and impulse
3 Pressure and stress
4 Power and strain
Explanation:
\({[P]=\left[{ML}^{-1} {~T}^{-3}\right]}\) But strain is dimensionless. So correct option is (4)
PHXI02:UNITS AND MEASUREMENTS
367347
The dimension of mass is zero in the following physical quantities.
1 Surface tension
2 Coefficient of viscosity
3 Heat
4 Specific heat capacity
Explanation:
Conceptual Question
PHXI02:UNITS AND MEASUREMENTS
367348
Which one of the following is NOT correct?
1 Dimensional formula of thermal conductivity (\(K\)) is \({M^1}{L^1}{T^{ - 3}}{K^{ - 1}}\)
2 Dimensional formula of potential (\(V\)) is \({M^1}{L^2}{T^3}{A^{ - 1}}\)
3 Dimensional formula of permeability of free space \(({\mu _0})\) is \({M^1}{L^2}{T^{ - 2}}{A^{ - 2}}\)
4 Dimensional formula of \(RC\) is \({M^0}{L^0}{T^{ - 1}}\)
Explanation:
Thermal conductivity \({\text{ = }}\frac{{{\text{Heat}}\;{\text{energy}}\; \times \;{\text{thickness}}}}{{{\text{Area}}\; \times \;{\text{Temperature}}\; \times \;{\text{time}}}}\) \([K] = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ {{L^2}} \right]\left[ K \right]\left[ T \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 3}}{K^{ - 1}}} \right]\) Potential \( = \frac{{Work}}{{Charge}}\) \([V] = \frac{{M{L^2}{T^{ - 2}}}}{{\left[ {AT} \right]}}\; = \;\left[ {{M^1}{L^2}{T^{ - 3}}{A^{ - 1}}} \right]\) Permeability of free space \({\text{ = }}\frac{{{\text{force}}\; \times \;{\text{distance}}}}{{{\text{current}}\; \times \;{\text{current}}\; \times \;{\text{length}}}}\) \(\left[ {{\mu _0}} \right]\; = \;\frac{{\left[ {ML{T^{ - 2}}} \right]\left[ L \right]}}{{\left[ A \right]\left[ A \right]\left[ L \right]}}\; = \;\left[ {{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}} \right]\) \(RC\) is the time constant of \(RC\) circuit. \([RC] = [{M^0}{L^0}{T^1}]\)
