Assertion- Vector product of two vectors is an axial vector-Reason- For a body under rotation- if v- instantaneous velocity- r- radius vector and - angular velocity- then - v-r-

Axial vector is a vector which nbsp;does not change its sign on changing nbsp;the coordinate system to a new system by a reflection in the origin. When the ...

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Standard XII

Physics

Relation between Linear and Angular Speed

Assertion: Ve...

Question

Assertion: Vector product of two vectors is an axial vector.
Reason: For a body under rotation, if $\to v =$ instantaneous velocity, $\to r =$ radius vector and $\to ω =$ angular velocity, then $\to ω = \to v \times \to r$ .

If both assertion and reason are true and reason is the correct explanation of assertion.

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If both assertion and reason are true and reason is not the correct explanation of assertion.

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If assertion is true but reason is false

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If both assertion and reason are false

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Solution

The correct option is C If assertion is true but reason is false
Axial vector is a vector which does not change its sign on changing the coordinate system to a new system by a reflection in the origin.
When the direction of the coordinate axes are inverted, the cross product of two vectors will not change sign. Hence cross product of two vectors is an axial vector.

We also know that the relation between linear and angular velocity is,
$\to v = \to ω \times \to r$

Hence reason is false.

Option C is the correct answer.

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Similar questions

Q. The velocity of the rotating body is given by

\to V = \to ω \times \to r,

where

\to ω

is the angular velocity and

\to r

is the radius vector. The angular velocity of a body is

\to ω =^i - 2^j + 2^k

and the radius vector

\to r = 4^j - 3^k,

then

| \to V |

Q. Assertion: Vector product of two vectors is an axial vector.
Reason: For a body under rotation, if

\to v =

instantaneous velocity,

\to r =

radius vector and

\to ω =

angular velocity, then

\to ω = \to v \times \to r

Q. Write vector relation between angular velocity

(\to ω)

, tangential velocity

(\to V)

and position vector

(\to r)

Q. For a body, angular velocity

\to ω =^i - 2^j + 3^k

and radius vector

\to r =^i +^j +^k

, then its velocity is :-

Q. The velocity of the rotating body is given by

\to V = \to ω \times \to r,

where

\to ω

is the angular velocity and

\to r

is the radius vector. The angular velocity of a body is

\to ω =^i - 2^j + 2^k

and the radius vector

\to r = 4^j - 3^k,

then

| \to V |

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Assertion: Vector product of two vectors is an axial vector. Reason: For a body under rotation, if →v= instantaneous velocity, →r= radius vector and →ω= angular velocity, then →ω=→v×→r.

Assertion: Vector product of two vectors is an axial vector.
Reason: For a body under rotation, if $\to v =$ instantaneous velocity, $\to r =$ radius vector and $\to ω =$ angular velocity, then $\to ω = \to v \times \to r$ .