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Question

A force F=α^i+3^j+6^k is acting at a point r=2^i6^j12^k. The value of α for which angular momentum about origin is conserved is

A
1
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B
2
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C
Zero
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D
1
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Solution

The correct option is A 1
Given,
F=α^i+3^j+6^k..... (1)
r=2^i6^j12^k ....(2)
We know for angular momentum to remain conserved, torque of force has to be zero.
τ=0
r×F=0 [τ=r×F]
∣ ∣ ∣^i^j^k2612α36∣ ∣ ∣=0
^i(36+36)^j(12+12α)+^k(6+6α)=0
12+12α=0 or 6+6α=0
α=1
The value of α is 1 for which angular momentum about origin is conserved.

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