Question

Two physical quantities of which one is a vector and the other is a scalar having the same dimensional formula are
A. Work and energy
B. Torque and work
C. impulse and momentum
D. Power and pressure

Answer 1

Cross product of two vectors is a vector and dot product of two vectors is scalar. The concept of vector and scalar quantities information is must to the students.

Complete step by step solution:
Vector quantity: We need both magnitude and direction to define that physical quantity and follow vector laws of addition that physical quantity is called vector quantities like; Force, Torque, etc.

Scalar quantity: We need only magnitude physical quantities called scalar like distance, work, energy.

Tensor: It is a special type of physical quantities that have both magnitude and direction but it does not follow the vector laws of addition.

Now,
Torque is the turning effect of force and is a vector quantity. It depends on the magnitude of the force and its perpendicular distance from the line of action.

$$(\overrightarrow C = \overrightarrow {F\,} \, \times \,\overrightarrow r ) \to Vector \\\ \\\$$

Work done is the dot product of force and displacement vectors. Thus work done is a scalar quantity i.e. $W:\overrightarrow F \,\overrightarrow S$
$\Rightarrow$Unit of torque and work is the same Nm or Joule.

Therefore dimension of torque is same as work i.e. $[M{L^2}{T^{ - 2}}]$
Hence, (B) is correct option.

Additional information: Torque is defined as the measure of the force that can cause an object to rotate about an axis. Torque causes angular acceleration.

Note: Torque is the cross product of force and perpendicular distance from the line of action and work done is the dot product of force and displacement.