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Which of the following quantities are independent of the choice of inertial frame? (There may be more than one correct answer.)

Which of the following quantities are independent of the choice of inertial frame? (There may be more than one correct answer.)

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
The correct option is (D) work.
Below figure shows a bead slides without friction along a thin horizontal rod. The bead moves from A to B, which we represent by the displacement vectors.

233-2420_1.JPG
A constant force F is exerted on the bead by an external agent; F makes an angle ? with the displacement vector: Only the component of the force F cos ? along the displacement vector contributes to the work, so the work done by the force F is
233-1114_1.JPG
233-1811_1.JPG
Work is a scalar, and scalars do not have components. It may appear from equation (2) that the value of the work depends on where we draw the coordinate axes; however equation (1) shows that this is not true. In general, the value of the dot product is independent of the choice of the coordinate axes. From the above observation we conclude that, work is independent of the choice of inertial frame. Thus, option (D) is correct.

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