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Question
Figure shows two identical particles 1 and 2, each of mass m, moving in opposite directions with same speed v along parallel lines. At a particular instant, r1 and r2 are their respective position vectors drawn from point A which is in the plane of the parallel lines. Choose the correct options:
- Angular momentum l1 of particle 1 about A is l1 = mvd1
- Angular momentum l2 of particle 2 about A is l2 = mvr2
- Total angular momentum of the system about A is l = mv(r1 + r2)
- Total angular momentum of the system about A is l = mv (d2 − d1)
⊗ represents a unit vector coming out of the page.
⊗ represents a unit vector going into the page.
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Solution
a and b
Explanation:
The angular momentum L of a particle with respect to the origin is defined to be L = r × p where r is the position vector of the particle and p is the linear momentum. The direction of L is perpendicular to both d r and p by the right-hand rule.
For particle 1, I1 = r1 × mv, is out of the plane of the paper and perpendicular to r1 and p(mv) Similarly I2 = r2 × m(– v) is into the plane of the paper and perpendicular to r2 and – p.
Hence, total angular momentum
`l = l_1 + l_2 = r_1 xx mv + (- r_2 xx mv)`
`|l| = mvd_1 - mvd_2` as `d_2 > d_1`, total angular momentum will be inward
Hence, I = mv(d2 – d1) ⊗.
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