The linear velocity of a rotating body is given by →v=→ω×→r, where →ω is the angular velocity and →r is the radius vector. The angular velocity of a body is →ω=^i−2^j+2^k and the radius vector →r=4^j−3^k, then ∣∣→v∣∣ is
A
√29 units
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B
√31 units
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C
√37 units
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D
√41 units
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Solution
The correct option is A√29 units We know that, →v=→ω×→r=(^i−2^j+2^k)×(4^j−3^k)
→v=∣∣
∣
∣∣^i^j^k1−2204−3∣∣
∣
∣∣
→v=−2^i+3^j+4^k Thus, the magnitude of →v is,∣∣→v∣∣=√(−2)2+32+42=√29 units