Question

Displacement \( x^i \) is a contravariant vector. The work done by a force is an invariant scalar. Therefore, force and hence momentum are:

• A. Both covariant vectors
• B. Both contravariant vectors
• C. A mixed tensor of rank 2 and a contravariant vector respectively
• D. A covariant vector and a contravariant vector respectively

Hint:

In relativity, four-force and four-momentum are both contravariant vectors.

Answer 1

The Correct Option is B

In tensor notation:
- Displacement \( x^i \) is a contravariant vector.
- Force \( F^i \) transforms the same way as displacement, so it is also contravariant.
- Work done \( W = F^i x_i \) is a scalar, which remains invariant.
Since both force and momentum transform as contravariant vectors.