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What is the optimum speed ($v_o$) for a car on a banked road of radius R and banking angle $\theta$ to avoid wear and tear on its tires?
The NCERT text states that at optimum speed, frictional force is not needed at all. The formula given is '$v_o = (R g \tan\theta)^{1/2}$'.
A car is moving on a banked road. For the optimum speed, what is the role of frictional force?
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.'
If the time interval $\Delta t \to 0$ for an object in circular motion, the average acceleration becomes the instantaneous acceleration. In this scenario, the instantaneous acceleration is directed:
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.
Consider a car on a level road taking a circular turn. If $v$ is the speed, $R$ is the radius, and $\mu_s$ is the coefficient of static friction, the condition for the car not to slip is:
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.
For a rigid body rotating about a fixed axis, which of the following quantities is the same for all particles of the body?
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.'
When an object moves in uniform circular motion, what can be said about its average speed compared to the magnitude of its average velocity over a given time interval?
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.
Which of the following conditions must be met for resonance to occur in a series LCR circuit?
According to the NCERT text, 'In a RLC circuit, resonance phenomenon occur when $X_L = X_C$ or $\omega_0 = 1/\sqrt{LC}$. For resonance to occur, the presence of both L and C elements in the circuit is a must.'
At resonance in a series LCR circuit, what is the relationship between the voltages across the inductor (L) and the capacitor (C)?
The NCERT text states, 'It is important to note that resonance phenomenon is exhibited by a circuit only if both L and C are present in the circuit. Only then do the voltages across L and C cancel each other (both being out of phase).'
What is the primary characteristic of the current amplitude at the resonant frequency in a series LCR circuit?
The context mentions, 'At resonant frequency, the current amplitude is maximum; $i_m = v_m/R$.'
Which of the following circuits CANNOT exhibit resonance?
The NCERT text clearly states, 'This means that we cannot have resonance in a RL or RC circuit.' This is because for resonance, both L and C must be present.
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.