Mechanical Properties Of Fluids

Step 1: Definition of coefficient of restitution.

Step 2: Using conservation of momentum.
Initial momentum:

Step 3: Calculating coefficient of restitution.
Since particle of mass stops after collision:

Step 4: Substituting value of .

Step 5: Conclusion.
The coefficient of restitution is .

Step 1: Identify total resistance.
The resistances and are in series.

Step 2: Case I — Current in anticlockwise direction.
Applying Kirchhoff’s loop law:
Magnitude of .

Step 3: Case II — Current in clockwise direction.
Now the sources oppose each other:

Step 4: Conclusion.
The value of is for anticlockwise current and for clockwise current.

Step 1: Formula for Volume Change.
The change in volume due to pressure is related to the bulk modulus by the formula: where is the bulk modulus and is the change in pressure. The pressure change at a depth is . Substituting, we get: Step 2: Solving for Depth.
We are given that the volume change is 0.2%, or . Solving for , we get: Substituting the known values: Step 3: Final Answer.
Thus, the depth at which the volume will decrease by 0.2% is 200 m.

Step 1: Definition of average acceleration.

Step 2: Change in velocity after half revolution.
After half revolution, velocity reverses direction. Hence,

Step 3: Time taken for half revolution.

Step 4: Calculating average acceleration.

Step 5: Conclusion.
The magnitude of average acceleration is .

Step 1: Expression for capillary rise.
Capillary rise is given by: Hence, .
Step 2: Value of acceleration due to gravity at depth .
Acceleration due to gravity at depth is: Step 3: Relation between and .
Step 4: Substitute value of .

Step 1: Define angle of contact.
Angle of contact is the angle between the tangent to the liquid surface at the point of contact and the solid surface, measured inside the liquid.
Step 2: Nature of angle of contact.
For a given solid–liquid pair and given surrounding medium, the angle of contact remains constant.
Step 3: Check each option.
- Pure water wets glass, so is small but greater than .
- Mercury does not wet glass, hence .
- Kerosene wets glass, so .
Step 4: Identify the incorrect statement.
Statement (A) is wrong because angle of contact is constant for a particular solid–liquid pair.