In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider following statements:
A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.
Analyze each statement.
A: Incorrect, as the graph is not a parabola but rather a more complex function of radius and viscosity.
B: Incorrect, as terminal velocity varies with ball size and density.
C: Correct, as viscosity and terminal velocity are temperature-dependent.
D: Correct, as variations in terminal velocity can reflect differences in liquid density.
E: Correct, as the initial speed affects the drag force and settling time, influencing the measured viscosity.
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):
Which of the following statements are true?
A. The same Bernoulli's equation is applicable to all the points in the flow field if the flow is irrotational.
B. The value of "Constant in the Bernoulli's equation" is different for different streamlines if the flow is rotational.
C. When a nozzle is fitted at the end of a long pipeline, the discharge increases.
D. The velocity of flow at the nozzle end is more than that in the case of a pipe without a nozzle, the head in both cases being the same.
Choose the most appropriate answer from the options given below:
The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.
The least acidic compound, among the following is
Choose the correct set of reagents for the following conversion: