The Torque - on a body about a given point is found to be equal to A-L - where A is the constant vector and L is the force on the body about that point- From this it follows that-

The correct options are A the magnitude of L⃗ does not change with time B dL⃗dt is perpendicular to L⃗ at all instants of time C the component ...

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Byju's Answer

Standard X

Physics

Translational and Rotational Equilibrium

The Torque ...

Question

The Torque $\to τ$ on a body about a given point is found to be equal to $\to A \times \to L$ , where $\to A$ is the constant vector and $\to L$ is the force on the body about that point. From this it follows that:

\frac{d \to L}{d t}

is perpendicular to

\to L

at all instants of time

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the component of

\to L

in the direction of

\to A

does not change with time

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the magnitude of

\to L

does not change with time

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\to L

does not change with time.

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Solution

The correct options are
A the magnitude of $\to L$ does not change with time
B $\frac{d \to L}{d t}$ is perpendicular to $\to L$ at all instants of time
C the component of $\to L$ in the direction of $\to A$ does not change with time
$τ = \to A \times \to L$
$∴ \frac{\to d L}{d t} = \to A \times \to L$
Since RHS is a vector perpendicular both $\to A$ and $\to L$
$\frac{\to d L}{d t} ⊥ \to A$ and $\frac{\to d L}{d t} ⊥ \to L$
Since $\frac{\to d L}{d t} ⊥ \to L$ , $∣ ∣ \to L ∣ ∣$ does not change with time.
Since $\frac{\to d L}{d t} ⊥ \to A$ , component of $\to L$ in the direction of $\to A$ does not change with time.

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Similar questions

Q. The torque

τ

on a body about a given point is found to be equal to

\to A \times \to L

, where

\to A

is a constant vector and

\to L

is the angular momentum of the body about the point. From this, it follows that

τ = \frac{d \to L}{d t}

(where

L

is the angular momentum and

t

is time).
a)

\to A

is perpendicular to

\to L

at all instants of time.
b) The component of

\to L

in the direction of

\to A

does not change with time.
c) The magnitude of

\to L

does not change with time.
d)

\to L

does not change with time.

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\to A \times \to L

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\to A

is a constant vector and

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Q. The torque

\to τ

on a body about a given point is found to be equal to

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is a constant vector and

\to L

is the angular momentum of the body about that point. From this it follows that :

Q. The torque

\to τ

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\to A

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The Torque →τ on a body about a given point is found to be equal to →A×→L , where →A is the constant vector and →L is the force on the body about that point. From this it follows that:

The Torque $\to τ$ on a body about a given point is found to be equal to $\to A \times \to L$ , where $\to A$ is the constant vector and $\to L$ is the force on the body about that point. From this it follows that: