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Rotational Motion

JEE Main level, single correct, medium

194 of 280

Question 194 of 280

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

Show answer and solution

Answer: (B) $10^{5}$

Mass of each car

m = 10^3

kg.
Speed of car

A

v_A = 72

km/h

= 72 \times \frac{5}{18} = 20

m/s.
Speed of car

B

v_B = 36

km/h

= 36 \times \frac{5}{18} = 10

m/s.
Relative velocity of car

A

with respect to car

B

v_{AB} = v_A - v_B = 20 - 10 = 10

m/s.
The cars are moving on parallel tracks separated by a perpendicular distance

d = 10

m.
The magnitude of angular momentum of car

A

with respect to car

B

is given by

L = m \times v_{AB} \times d

.
Substituting the values:

L = 10^3 \times 10 \times 10 = 10^5

J.s.
Thus, the correct option is (2).

JEE Main question paper PDF

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