Using the expression for energy stored in an inductor, \(U = \frac{1}{2}L{I^2},\) dimensions of mutual inductance or self inductance can be given by \(\left[ L \right] = \frac{{\left[ U \right]}}{{\left[ {{I^2}} \right]}} = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{\left[ {{I^2}} \right]}} = \left[ {M{L^2}{T^{ - 2}}{I^{ - 2}}} \right]\)
MHTCET - 2019
PHXI02:UNITS AND MEASUREMENTS
367351
Which of the following pairs of physical quantities do not have same dimensional formula?
1 Tension and surface tension
2 Work and torque
3 Impulse and linear momentum
4 Angular momentum and Planck’s constant
Explanation:
Because, dimension formula of tension same as force \( = [ML{T^{ - 2}}]\) and surface tension \({\rm{ = }}\frac{{{\rm{force}}}}{{{\rm{length}}}}\) \( = [M{L^0}{T^{ - 2}}]\) Work and torque, both are product of force and length. Impulse is equal to change in momentum.
NCERT Exemplar
PHXI02:UNITS AND MEASUREMENTS
367352
\(\left[M L^{2} T^{-3}\right]\) represents the dimensions of
1 pressure
2 energy
3 power
4 force
Explanation:
\([\) Power \(]=\dfrac{[\text { Work }]}{[\text { Time }]}=\dfrac{[\text { Force } \times \text { distance }]}{[\text { Time }]}\) \(=\dfrac{\left[M L T^{-2} \times L\right]}{[T]}=\left[M L^{2} T^{-3}\right] .\)
Using the expression for energy stored in an inductor, \(U = \frac{1}{2}L{I^2},\) dimensions of mutual inductance or self inductance can be given by \(\left[ L \right] = \frac{{\left[ U \right]}}{{\left[ {{I^2}} \right]}} = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{\left[ {{I^2}} \right]}} = \left[ {M{L^2}{T^{ - 2}}{I^{ - 2}}} \right]\)
MHTCET - 2019
PHXI02:UNITS AND MEASUREMENTS
367351
Which of the following pairs of physical quantities do not have same dimensional formula?
1 Tension and surface tension
2 Work and torque
3 Impulse and linear momentum
4 Angular momentum and Planck’s constant
Explanation:
Because, dimension formula of tension same as force \( = [ML{T^{ - 2}}]\) and surface tension \({\rm{ = }}\frac{{{\rm{force}}}}{{{\rm{length}}}}\) \( = [M{L^0}{T^{ - 2}}]\) Work and torque, both are product of force and length. Impulse is equal to change in momentum.
NCERT Exemplar
PHXI02:UNITS AND MEASUREMENTS
367352
\(\left[M L^{2} T^{-3}\right]\) represents the dimensions of
1 pressure
2 energy
3 power
4 force
Explanation:
\([\) Power \(]=\dfrac{[\text { Work }]}{[\text { Time }]}=\dfrac{[\text { Force } \times \text { distance }]}{[\text { Time }]}\) \(=\dfrac{\left[M L T^{-2} \times L\right]}{[T]}=\left[M L^{2} T^{-3}\right] .\)
Using the expression for energy stored in an inductor, \(U = \frac{1}{2}L{I^2},\) dimensions of mutual inductance or self inductance can be given by \(\left[ L \right] = \frac{{\left[ U \right]}}{{\left[ {{I^2}} \right]}} = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{\left[ {{I^2}} \right]}} = \left[ {M{L^2}{T^{ - 2}}{I^{ - 2}}} \right]\)
MHTCET - 2019
PHXI02:UNITS AND MEASUREMENTS
367351
Which of the following pairs of physical quantities do not have same dimensional formula?
1 Tension and surface tension
2 Work and torque
3 Impulse and linear momentum
4 Angular momentum and Planck’s constant
Explanation:
Because, dimension formula of tension same as force \( = [ML{T^{ - 2}}]\) and surface tension \({\rm{ = }}\frac{{{\rm{force}}}}{{{\rm{length}}}}\) \( = [M{L^0}{T^{ - 2}}]\) Work and torque, both are product of force and length. Impulse is equal to change in momentum.
NCERT Exemplar
PHXI02:UNITS AND MEASUREMENTS
367352
\(\left[M L^{2} T^{-3}\right]\) represents the dimensions of
1 pressure
2 energy
3 power
4 force
Explanation:
\([\) Power \(]=\dfrac{[\text { Work }]}{[\text { Time }]}=\dfrac{[\text { Force } \times \text { distance }]}{[\text { Time }]}\) \(=\dfrac{\left[M L T^{-2} \times L\right]}{[T]}=\left[M L^{2} T^{-3}\right] .\)
Using the expression for energy stored in an inductor, \(U = \frac{1}{2}L{I^2},\) dimensions of mutual inductance or self inductance can be given by \(\left[ L \right] = \frac{{\left[ U \right]}}{{\left[ {{I^2}} \right]}} = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{\left[ {{I^2}} \right]}} = \left[ {M{L^2}{T^{ - 2}}{I^{ - 2}}} \right]\)
MHTCET - 2019
PHXI02:UNITS AND MEASUREMENTS
367351
Which of the following pairs of physical quantities do not have same dimensional formula?
1 Tension and surface tension
2 Work and torque
3 Impulse and linear momentum
4 Angular momentum and Planck’s constant
Explanation:
Because, dimension formula of tension same as force \( = [ML{T^{ - 2}}]\) and surface tension \({\rm{ = }}\frac{{{\rm{force}}}}{{{\rm{length}}}}\) \( = [M{L^0}{T^{ - 2}}]\) Work and torque, both are product of force and length. Impulse is equal to change in momentum.
NCERT Exemplar
PHXI02:UNITS AND MEASUREMENTS
367352
\(\left[M L^{2} T^{-3}\right]\) represents the dimensions of
1 pressure
2 energy
3 power
4 force
Explanation:
\([\) Power \(]=\dfrac{[\text { Work }]}{[\text { Time }]}=\dfrac{[\text { Force } \times \text { distance }]}{[\text { Time }]}\) \(=\dfrac{\left[M L T^{-2} \times L\right]}{[T]}=\left[M L^{2} T^{-3}\right] .\)