Physics MCQs for NEET — Practice Questions with Answers

The NCERT text clarifies: 'Eq. (6.30a) and Eq. (6.30b), both, are vector equations. They are equivalent to three scalar equations each. Eq. (6.30a) corresponds to $\sum F_{ix} = 0$, $\sum F_{iy} = 0$ and $\sum F_{iz} = 0$. Similarly, Eq. (6.30b) is equivalent to three scalar equations $\sum \tau_{ix} = 0$, $\sum \tau_{iy} = 0$ and $\sum \tau_{iz} = 0$.'

The text states: 'The total torque on the body may not vanish. Such a torque changes the rotational state of motion of the rigid body, i.e. it changes the total angular momentum of the body in accordance with Eq. (6.28 b).'

The NCERT text explicitly states: 'Henceforth we shall omit the adjective 'external' because unless stated otherwise, we shall deal with only external forces and torques.'

The NCERT summary point 3 states: 'In rotation about a fixed axis, every particle of the rigid body moves in a circle which lies in a plane perpendicular to the axis and has its centre on the axis. Every Point in the rotating rigid body has the same angular velocity at any instant of time.'

For rotational equilibrium, the total torque must be zero ($\sum \vec{\tau_i} = 0$). For 'not in translational equilibrium', the total force must be non-zero ($\sum \vec{F_i} \neq 0$). This combination corresponds to the description of partial equilibrium provided in the text, specifically the example with Fig. 6.20(a) where the rod was in rotational equilibrium ($net moment = 0$) but not translational equilibrium ($\sum F \neq 0$).

According to the NCERT text, 'A unit vector is a vector of unit magnitude and points in a particular direction. It has no dimension and unit. It is used to specify a direction only.' Therefore, the statement that unit vectors have specific dimensions and units is incorrect.

The NCERT text states, 'Thus, $\vec{A} = A_x \hat{i} + A_y \hat{j}$.' This equation correctly represents a vector in terms of its components along the x and y axes using unit vectors.

According to equation 3.10 in the NCERT text, 'In general, a vector A can be written as $\vec{A} = |A| \hat{n}$ where $\hat{n}$ is a unit vector along A.'

A unit vector is used to specify direction. Multiplying a unit vector by a scalar changes its magnitude, not its direction (unless the scalar is negative, which reverses the direction). The NCERT states: 'If we multiply a unit vector, say $\hat{n}$ by a scalar $\lambda$, the result is a vector $\lambda \vec{n}$.'

The NCERT text explicitly states: 'We draw lines from the head of A perpendicular to the coordinate axes as in Fig. 3.9(b), and get vectors $\vec{A_1}$ and $\vec{A_2}$ such that $\vec{A_1} + \vec{A_2} = \vec{A}$'.