Practice free Rotational Motion (Physics) NEET multiple-choice questions online with instant answers and detailed explanations. No login required.
Which of the following statements is TRUE regarding the vector product?
The NCERT text highlights: 'The vector product, however, is not commutative.' It further illustrates this with '$\vec{j} \times \vec{i} = -\vec{k}$' whereas '$\vec{i} \times \vec{j} = \vec{k}$'.
If $\vec{a} = 3\hat{i} + 4\hat{j} - 5\hat{k}$ and $\vec{b} = -2\hat{j} + 3\hat{k}$, what is the value of $\vec{a} \cdot \vec{b}$?
The scalar product (dot product) is calculated as $A_x B_x + A_y B_y + A_z B_z$. Given $\vec{a} = 3\hat{i} + 4\hat{j} - 5\hat{k}$ and $\vec{b} = 0\hat{i} - 2\hat{j} + 3\hat{k}$, then $\vec{a} \cdot \vec{b} = (3)(0) + (4)(-2) + (-5)(3) = 0 - 8 - 15 = -23$. This is based on Example 6.4 which asks for both scalar and vector product, but only shows the calculation for scalar product (dot product).
For unit vectors $\hat{i}$, $\hat{j}$, and $\hat{k}$, which of the following is correct?
The NCERT text lists the results: '(i) $\hat{i} \times \hat{i} = 0, \hat{j} \times \hat{j} = 0, \hat{k} \times \hat{k} = 0$' and '(ii) $\hat{i} \times \hat{j} = \hat{k}$, $\hat{j} \times \hat{k} = \hat{i}$, $\hat{k} \times \hat{i} = \hat{j}$.' Based on this, option o3 is correct.
If $\vec{a} = a_x\hat{i} + a_y\hat{j} + a_z\hat{k}$ and $\vec{b} = b_x\hat{i} + b_y\hat{j} + b_z\hat{k}$, the vector product $\vec{a} \times \vec{b}$ can be expressed in determinant form as:
The NCERT text provides the determinant form: '$\vec{a} \times \vec{b} = |\begin{smallmatrix} \hat{i} & \hat{j} & \hat{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{smallmatrix}|$.'
The time rate of change of the angular momentum of a particle is equal to:
The NCERT text states: 'Thus, the time rate of change of the angular momentum of a particle is equal to the torque acting on it. This is the rotational analogue of the equation $\vec{F} = d\vec{p}/dt...$'
If $\vec{r}$ is the position vector and $\vec{p}$ is the linear momentum of a particle, its angular momentum $\vec{l}$ is given by:
The NCERT text defines angular momentum: '$\vec{l} = \vec{r} \times \vec{p}$.'
If $\vec{v}$ is the linear velocity and $\vec{\omega}$ is the angular velocity for a particle in rotational motion, their relation is given by:
The NCERT text mentions: 'The linear velocity of the particle at P is $\vec{v} = \vec{\omega} \times \vec{r}$'.
The angular velocity vector $\vec{\omega}$ for rotation about a fixed axis lies:
The NCERT text states: 'For rotation about a fixed axis, the angular velocity vector lies along the axis of rotation, and points out in the direction in which a right handed screw would advance...'
The vector product of two parallel vectors is:
The magnitude of the vector product is $ab\sin\theta$. If two vectors are parallel, $\theta = 0^\circ$ or $\theta = 180^\circ$. In both cases, $\sin\theta = 0$. Therefore, the magnitude of the vector product is zero, making it a zero vector. The text states: 'd(r $\times$ p)/dt = r $\times$ dp/dt + dr/dt $\times$ p. Now, the velocity of the particle is v = dr/dt and p = m v. Because of this d(r $\times$ p)/dt = r $\times$ dp/dt + v $\times$ mv. The term v $\times$ mv is zero as the vector product of two parallel vectors vanishes.'
Which of the following statements is TRUE regarding the center of mass of a system of particles?
According to the NCERT text, 'The centre of mass moves as if all the mass of the system is concentrated at this point and all the external forces act at it.' This is a fundamental concept in the motion of the center of mass.
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