The linear velocity of a rotating body is given by v = vecω × r . The angular velocity of body is vecω=5 hat i -4 hat j +9 hat k and the radius vector r =8 hat i -6 hat j +3 hat k then | V | is:

Question

The linear velocity of a rotating body is given by v = vecω × r . The angular velocity of body is vecω=5 hat i -4 hat j +9 hat k and the radius vector r =8 hat i -6 hat j +3 hat k then | V | is: (A) 70.8 units (B) 90 units (C) √149 units (D) √2017 units

Tardigrade Admin · Accepted Answer

As, V = vecω × r , then vecV=| beginarrayccc hati hatj hat k 5 -4 +9 8 -6 3 endarray| V = hat i (-12-(-54)- hat j (15-72)+ hat k (-30-(-32))) V =42 hat i -57 hat j +2 hat k | V |=√(42)2+(57)2+(2)2 | V |=√5017=70.8 unit

Q. The linear velocity of a rotating body is given by $v = ω \times r$ . The angular velocity of body is $ω = 5 \hat{i} - 4 \hat{j} + 9 \hat{k}$ and the radius vector $r = 8 \hat{i} - 6 \hat{j} + 3 \hat{k}$ then $∣ V ∣$ is:

$70.8$ units

$90$ units

$149$ units

$2017$ units

As, $V = ω \times r,$ then
$V = ∣ ∣ \hat{i} 58 \hat{j} - 4 - 6 \hat{k} + 9 3 ∣ ∣$
$V = \hat{i} (- 12 - (- 54) - \hat{j} (15 - 72) + \hat{k} (- 30 - (- 32)))$
$V = 42 \hat{i} - 57 \hat{j} + 2 \hat{k}$
$∣ V ∣ = (42)^{2} + (57)^{2} + (2)^{2}$
$∣ V ∣ = 5017 = 70.8$ unit

Q. The linear velocity of a rotating body is given by v=ω×r . The angular velocity of body is ω=5i^−4j^​+9k^ and the radius vector r=8i^−6j^​+3k^ then ∣V∣ is:

70.8 units

90 units

149​ units

2017​ units