Two bodies and have masses and

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two bodies

A

and

B

have masses

4\,\text{kg}

and

3\,\text{kg}

, respectively. Their momenta are

\mathbf{p}_A = 8\,\text{kg m/s}\,\mathbf{i}

and

\mathbf{p}_B = 12\,\text{kg m/s}\,\mathbf{j}

. Which statement correctly describes the combined mass and momentum of the system? (a) The combined mass is a scalar equal to

7\,\text{kg}

, and the resultant momentum is a scalar of magnitude

20\,\text{kg m/s}

obtained by adding the magnitudes. (b) The combined mass is the vector

(4\mathbf{i}+3\mathbf{j})\,\text{kg}

, while the resultant momentum is the vector

(8\mathbf{i}+12\mathbf{j})\,\text{kg m/s}

. (c) The combined mass is a scalar equal to

7\,\text{kg}

, and the resultant momentum is the vector

(8\mathbf{i}+12\mathbf{j})\,\text{kg m/s}

. (d) The combined mass is a scalar equal to

5\,\text{kg}

(obtained using Pythagoras on the individual masses), and the total momentum has magnitude

14\,\text{kg m/s}