Which pair do not have equal dimensions?

• A. Energy and torque
• B. Force and impulse
• C. Angular momentum and Planck's constant
• D. Elastic modulus and pressure

To determine which pair does not have equal dimensions, let's examine each option closely.

Analysis of Each Pair

A. Energy and Torque

Energy has the dimension of [ML²T^-2], while torque has the dimension of [ML²T^-2] as well. Thus, these two have equal dimensions.

B. Force and Impulse

Force is measured in [MLT^-2], and impulse, which is force multiplied by time, has the dimension [MLT^-1]. Therefore, these two do not have equal dimensions.

C. Angular Momentum and Planck's Constant

Angular momentum has the dimension of [ML²T^-1], while Planck's constant is also expressed in [ML²T^-1]. Hence, these two are equal in dimensions.

D. Elastic Modulus and Pressure

Both elastic modulus and pressure share the dimension of [ML^-1T^-2], indicating they are equal in dimensions as well.

Final Conclusion

The pair that does not have equal dimensions is B. Force and Impulse.