Motion In A Plane

Question

The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at (2, 0, 3) about the point (2,-2,2), is given by

$- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$

$- 4 \hat{i} - \hat{j} - 8 \hat{k}$

$- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

$- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$

Solution

$- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

Moment of force,
$\vec{τ} = \vec{r} x \vec{F}$

$\vec{τ} = (\vec{r} - \vec{r_{0}}) x \vec{F} \vec{r} - \vec{r_{0}} = (2 \hat{i} + 0 \hat{j} - 3 \hat{k}) - (2 \hat{i} - 2 \hat{j} - 2 \hat{k}) = 0 \hat{i} + 2 \hat{j} - \hat{k} \vec{τ} = (0 \hat{i} + 2 \hat{j} - \hat{k}) (4 \hat{i} + 5 \hat{j} - 6 \hat{k}) \vec{τ} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 2 & - 1 \\ 4 & 5 & - 6 \end{matrix}| = - 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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Motion In A Plane

The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at (2, 0, 3) about the point (2,-2,2), is given by

$- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$

$- 4 \hat{i} - \hat{j} - 8 \hat{k}$

$- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

$- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

The moment of the force, F→ = 4i^ + 5j^ -6k^ at (2, 0, 3) about the point (2,-2,2), is given by -8i^ -4j^ -7k^ -4i^ -j^ -8k^ -7i^ -4j^ -8k^ -7i^ -8j^ -4k^

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$ at (2, 0, 3) about the point (2,-2,2), is given by

$- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}$

$- 4 \hat{i} - \hat{j} - 8 \hat{k}$

$- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

$- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}$

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.