Given- - -2- k and r- -2- i -2- j- Find the linear velocity-

The correct option is A 4∧ i +4∧ j Linear velocity of an object, v⃗=ω⃗×r⃗ where, ω⃗ is the angular velocity of object about a point r⃗ i ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Given, ω⃗ =...

Question

Given, $\to ω = 2 \land k$ and $\to r = 2 \land i + 2 \land j$ . Find the linear velocity.

4 \land i + 4 \land j

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4 \land i - 4 \land k

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- 4 \land i + 4 \land j

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- 4 \land i - 4 \land j

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Solution

The correct option is A $- 4 \land i + 4 \land j$
Linear velocity of an object, $\to v = \to ω \times \to r$
where, $\to ω$ is the angular velocity of object about a point
$\to r$ is the position vector of object from the point.
Thus, $\to v = (2^k) \times (2^i + 2^j)$
$= - 4^i + 4^j$

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\to r = i + 2 j + 3 k + λ (2 i + 3 j + 4 k)

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Given, →ω=2∧k and →r=2∧i+2∧j. Find the linear velocity.

The correct option is A −4∧i+4∧jLinear velocity of an object, →v=→ω×→rwhere, →ω is the angular velocity of object about a point→r is the position vector of object from the point.Thus, →v=(2^k)×(2^i+2^j) =−4^i+4^j

Given, $\to ω = 2 \land k$ and $\to r = 2 \land i + 2 \land j$ . Find the linear velocity.

The correct option is A $- 4 \land i + 4 \land j$
Linear velocity of an object, $\to v = \to ω \times \to r$
where, $\to ω$ is the angular velocity of object about a point
$\to r$ is the position vector of object from the point.
Thus, $\to v = (2^k) \times (2^i + 2^j)$
$= - 4^i + 4^j$