Two cars **A** and **B** each of mass $10^3$ kg are moving on parallel tracks separated by a distance of $10$ m, in same direction with speeds $72$ km/h and $36$ km/h. The magnitude of angular momentum of car **A** with respect to car **B** is ________ J·s.

Question

Accepted Answer

B. 1. Convert both speeds into SI units.

$$
   v_A=72	imes\frac{5}{18}=20\ \mathrm{m/s}
   $$

$$
   v_B=36	imes\frac{5}{18}=10\ \mathrm{m/s}
   $$

2. Since both cars move in the same direction, the relative velocity of car **A** with respect to car **B** is

$$
   \vec{v}_{AB}=\vec{v}_A-\vec{v}_B
   $$

Therefore,

$$
   v_{AB}=20-10=10\ \mathrm{m/s}
   $$

3. The angular momentum of a particle about a point is given by

$$
   \vec{L}=\vec{r}	imes\vec{p}
   $$

where $\vec{p}=m\vec{v}$.

4. Since the cars move on parallel tracks, the perpendicular distance between their lines of motion is

$$
   r_\perp=10\ \mathrm{m}
   $$

Hence,

$$
   L=m.v_{	ext{relative}}.r_\perp
   $$

5. Substitute the given values.

$$
   L=(10^3)	imes10	imes10
   $$

$$
   L=10^5\ \mathrm{J\cdot s}
   $$

6. Therefore, the magnitude of the angular momentum of car **A** with respect to car **B** is

$$
   10^5\ \mathrm{J\cdot s}.
   $$

7. Hence, the correct option is **B**.

Two cars A and B each of mass 10310^3103 kg are moving on parallel tracks separated by a distance of 101010 m, in same direction with speeds 727272 km/h and 363636 km/h. The magnitude of angular momentum of car A with respect to car B is ________ J·s.

Two cars A and B each of mass $10^3$ kg are moving on parallel tracks separated by a distance of $10$ m, in same direction with speeds $72$ km/h and $36$ km/h. The magnitude of angular momentum of car A with respect to car B is ________ J·s.