Motion in a Lane MCQs for NEET — Physics Questions with Answers

From the NCERT text, we have $v = 2\pi R \nu$. Substituting this into $a_c = v^2/R$, we get $a_c = (2\pi R \nu)^2 / R = 4\pi^2 R^2 \nu^2 / R = 4\pi^2 \nu^2 R$.

The NCERT text states that at optimum speed, frictional force is not needed at all. The formula given is '$v_o = (R g \tan\theta)^{1/2}$'.

According to the NCERT text, 'At this speed [optimum speed], frictional force is not needed at all to provide the necessary centripetal force. Driving at this speed on a banked road will cause little wear and tear of the tyres.'

The NCERT states, 'In Fig. 3.18(c), $\Delta t \to 0$ and the average acceleration becomes the instantaneous acceleration. It is directed towards the centre*.' The footnote clarifies, 'In the limit $\Delta t \to 0$, $\Delta r$ becomes perpendicular to r. In this limit $\Delta v \to 0$ and is consequently also perpendicular to V. Therefore, the acceleration is directed towards the centre, at each point of the circular path.' Since the velocity vector is tangential, the acceleration (towards the center) is perpendicular to the velocity.

The NCERT text mentions that for a car on a level road, $f_s \le \mu_s N$. Since $N = mg$ and $f_s = mv^2/R$, we have $mv^2/R \le \mu_s mg$. This simplifies to $v^2/R \le \mu_s g$, or $v^2 \le \mu_s R g$. This is the condition for not slipping.

The NCERT text states, 'We observe that at any given instant the relation $v = \omega r$ applies to all particles of the rigid body. ... We use the same angular velocity $\omega$ for all the particles. We therefore, refer to $\omega$ as the angular velocity of the whole body.'

The 'POINTS TO PONDER' section states, 'The average speed of an object is greater than or equal to the magnitude of the average velocity over a given time interval. The two are equal only if the path length is equal to the magnitude of displacement.' In circular motion, unless the time interval is zero, path length is generally greater than displacement, so average speed is greater or equal.

According to the NCERT text, 'A scalar quantity is a quantity with magnitude only. It is specified completely by a single number, along with the proper unit. Examples are: the distance between two points, mass of an object, the temperature of a body and the time at which a certain event happened.' Acceleration, velocity, and displacement are vector quantities as they have both magnitude and direction.

The NCERT text states, 'W e found that the directional aspect of these quantities can be taken care of by + and – signs, as in one dimension only two directions are possible.' Unit vectors are used for motion in two or three dimensions.

The NCERT text highlights, 'But in order to describe motion of an object in two dimensions (a plane) or three dimensions (space), we need to use vectors to describe the above-mentioned physical quantities. Therefore, it is first necessary to learn the language of vectors.'