Question 29: Work, Energy and Power & Circular Motion

Question

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.

Accepted Answer

Speed of car $A, v_A=72 	imes \frac{5}{18}=20 \mathrm{~m} / \mathrm{s}$
Speed of car B, $\mathrm{v}_{\mathrm{B}}=36 	imes \frac{5}{18}=10 \mathrm{~m} / \mathrm{s}$
Since both cars are moving in the same direction, the relative velocity of car $A$ with respect to $\operatorname{car} B\left(\vec{v}_{A B}ight)$ is :
$$ \overrightarrow{\mathrm{v}}_{\mathrm{AB}}=\overrightarrow{\mathrm{v}}_{\mathrm{A}}-\overrightarrow{\mathrm{v}}_{\mathrm{B}} $$
$$\Rightarrow $$ $\overrightarrow{\mathrm{v}}_{\mathrm{AB}}=20-10=10 \mathrm{~m} / \mathrm{s}$
Angular momentum of a point mass relative to an observer is defined as:
$$ \overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}} 	imes \overrightarrow{\mathrm{p}} $$
Where $\overrightarrow{\mathrm{r}}$ is the position vector and $\overrightarrow{\mathrm{p}}$ is the linear momentum ( $\mathrm{m} \overrightarrow{\mathrm{v}}$ ).
The perpendicular distance $\left(\mathrm{r}_{\perp}=\mathrm{d}ight)$ between the two parallel tracks:
$$ \mathrm{L}=\mathrm{m} \cdot \mathrm{v}_{	ext {relative }} \cdot \mathrm{r}_{\perp} $$
Given values are,
Mass $\mathrm{m}=10^3 \mathrm{~kg}$
Relative speed $\mathrm{v}_{\mathrm{AB}}=10 \mathrm{~m} / \mathrm{s}$
Perpendicular distance $\mathrm{r}_{\perp}=10 \mathrm{~m}$
Substituting the values into the formula :
$$ L=\left(10^3ight) 	imes(10) 	imes(10) $$
$$\Rightarrow $$ $$ \mathrm{L}=10^5 \mathrm{~J} . \mathrm{s} $$
Therefore, the angular momentum of the car A with respect to B is $10^5 \mathrm{~J}$. s.
Hence, the correct option is (B).

Answer

$3.6 	imes 10^{5}$

Answer

$10^{5}$

Answer

$3 	imes 10^{5}$

Answer

$2 	imes 10^{5}$

Work, Energy and Power & Circular Motion

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.

Choose the correct answer: