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Question

# A particle of mass m=5 kg is moving with a uniform speed 3√2 m/s in XY plane along the line y=x+4. The angular momentum about the origin is [in kg m2/s]

A
40
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B
60
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C
zero
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D
20
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Solution

## The correct option is B 60 Given, Mass of particle m=5 kg Speed of particle v=3√2 m/s As we know, L=mvr⊥ where r⊥ is the shortest /perpendicular distance, of the particle from the origin. As we know, Perpendicular distance between a point and a line is given by, r⊥=∣∣∣Ax1+Bx2+C√A2+B2∣∣∣=∣∣ ∣ ∣∣x−y+4√12+(−1)2∣∣ ∣ ∣∣=∣∣∣0−0+4√2∣∣∣ (substituting (x,y)=(0,0) for origin) r⊥=2√2 Therefore, from L=mvr⊥ L=5×3√2×2√2 L=60 kg m2/s

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