Question

Which one is the pseudo vector in the given options?
A. Linear momentum
B. Angular momentum
C. Force
D. All the above

Answer 1

Hint:The pseudo vector is the resultant vector of cross product of the two vectors. Recall the formulae for each of the options given and check which of the physical quantities is/are the resultant of a cross product and determine the pseudo vector amongst the given options.

Complete answer:
The linear momentum of an object is the product of the mass of the object and velocity of the object.
\[\vec P = m\vec v\]
The mass \[m\] in the above equation is a scale physical quantity and velocity \[\vec v\] is a vector physical quantity. Hence, the linear momentum vector \[\vec P\] is the product of a scalar and a vector and the linear momentum vector \[\vec P\] has the same direction as that of the velocity vector \[\vec v\].Therefore, linear momentum is not a pseudo vector and is a real or polar vector.Hence, the option A is incorrect.

The force acting on an object is the product of the mass of the object and acceleration of the object.
\[\vec F = m\vec a\]
The mass \[m\] in the above equation is a scale physical quantity and acceleration \[\vec a\] is a vector physical quantity. Hence, the force vector \[\vec F\] is the product of a scalar and a vector and the force vector \[\vec F\] has the same direction as that of the acceleration vector \[\vec a\].Therefore, force is not a pseudo vector and is a real or polar vector.Hence, the option C is incorrect.

The angular momentum of an object is the product of the position of the object and linear momentum of the object.
\[\vec L = \vec r \times \vec P\]
The position \[\vec r\] in the above equation is a vector quantity and linear momentum \[\vec P\] is also a vector quantity. Hence, the angular momentum vector \[\vec L\] is the cross product of the position vector \[\vec r\] and linear momentum vector \[\vec P\].
Therefore, angular momentum is the cross product of the position vector and linear momentum vector. Hence, it is a pseudo vector.

Hence, the correct option is B.

Note: One can also define the pseudo vectors as the angular vectors. From the given options, force and linear momentum are the linear vectors having the direction in a straight line. But the angular momentum is the vector having the direction along the axis of rotation of the rotating object and the object rotates about this axis of rotation. Hence, it is angular and pseudo vector.