SATHEE: Rotational Motion Question 64

Rotational Motion Question 64

Question: A particle of mass m moves in the XY plane with a velocity v along the straight line AB. if the angular momentum of the particle with respect to origin O is $L_{A}$ when it is at A and $L_{B}$ when it is at B, then:

[AIPMT (S) 2007]

Options:

A) $L_{A} > L_{B}$

B) $L_{A} = L_{B}$

C) the relationship between $L_{A}$ and $L_{B}$ depends upon the slope of the line AB

D) $L_{A} < L_{B}$

Show Answer

Answer:

Correct Answer: B

Solution:

From the definition of angular momentum,

$\vec{L} = \vec{r} \times \vec{p} = r m v \sin ϕ (- \vec{k})$

Therefore, the magnitude of L is

$L = m v r \sin ϕ = m v d$

where $d = r \sin ϕ$ is the distance of closest approach of the particle to the origin.

As d is same for both the particles, hence $L_{A} = L_{B}$ .

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Rotational Motion Question 64

Question: A particle of mass m moves in the XY plane with a velocity v along the straight line AB. if the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then:

Options:

Answer:

Solution:

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Question: A particle of mass m moves in the XY plane with a velocity v along the straight line AB. if the angular momentum of the particle with respect to origin O is $L_{A}$ when it is at A and $L_{B}$ when it is at B, then: