Which pair do not have equal dimensions ? (a) Energy and torque
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This is indeed confusing when you first encounter it, because there's an important difference between these quantities that isn't reflected in their notation. In early physics courses students are taught to rely a lot (too much IMO) on units, and in this case that fails.
The root of the issue here is that we are actually dealing with vector products when we arrive at the formulas for these quantities. The energy is a scalar dot product of the force vector and the displacement vector, while the torque is a vector cross product of a force vector and a distance vector. There is customarily no notation of the vector for torque, so there is ambiguity there.
The energy you are referring to is the energy required to move a body through a distance, and is given by force times distance along the direction of motion, while torque is force times a perpendicular distance, which means, by definition, there is no component of that force along the direction of motion.
Torques are analogous to forces rather than energy, and the relationship between torque and energy is expressed by [math]E = [/math][math]tau*theta[/math] where [math]tau[/math] is the torque and [math]theta[/math] is the angle the torque is applied through. Since radians are dimensionless, you still have the same units, but now you have included the (angular) distance the torque was applied through.
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The root of the issue here is that we are actually dealing with vector products when we arrive at the formulas for these quantities. The energy is a scalar dot product of the force vector and the displacement vector, while the torque is a vector cross product of a force vector and a distance vector. There is customarily no notation of the vector for torque, so there is ambiguity there.
The energy you are referring to is the energy required to move a body through a distance, and is given by force times distance along the direction of motion, while torque is force times a perpendicular distance, which means, by definition, there is no component of that force along the direction of motion.
Torques are analogous to forces rather than energy, and the relationship between torque and energy is expressed by [math]E = [/math][math]tau*theta[/math] where [math]tau[/math] is the torque and [math]theta[/math] is the angle the torque is applied through. Since radians are dimensionless, you still have the same units, but now you have included the (angular) distance the torque was applied through.
PLEASE MARK IT AS BRAINLIEST.
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