Mechanical Properties Of Solids

Step 1: Concept
Work done .
Step 2: Analysis
A soap bubble has two free surfaces (inner and outer). Surface area of one side . Total area change .
Step 3: Conclusion
.
Final Answer: (B)

Step 1: Reagent
Lucas reagent is a mixture of anhydrous and concentrated .
Step 2: Reaction
It reacts with alcohols to form alkyl chlorides, which appear as turbidity.
Step 3: Application
The test is used specifically to distinguish between primary, secondary, and tertiary alcohols based on the speed of turbidity formation.
Final Answer: (d)

Concept: Isothermal:

Step 1: Average pressure
Conclusion:

Concept: Spring constant varies inversely with length:

Step 1: Divide the spring.
Let shorter piece = , longer piece = Total length:

Step 2: Original spring.


Step 3: Long piece.


Step 4: Find ratio.

Concept: From Torricelli’s law: Time to empty tank:

Step 1: Relation.
For full height : For half height:

Concept: Young’s modulus:

Step 1: Strain in ring.


Step 2: Stress.


Step 3: Force.

Concept: Spring constant is inversely proportional to length:

Step 1: Use proportionality.


Step 2: Relate lengths.


Step 3: Find new spring constant.


Step 4: Correct interpretation.
Since the original spring behaves like two springs in series: Using , solving gives: