Free Body Diagram

Step 1: Concept
The net force is the vector sum of gravitational intensities from each mass.
Step 2: Analysis
At the centroid of an equilateral triangle with equal masses at the vertices, the forces are equal in magnitude and separated by .
Step 3: Conclusion
The vector sum because the resultant of any two is equal and opposite to the third.
Final Answer: (A)

Step 1: Apply Raoult's Law
For an ideal solution: .
Step 2: Identify Values
, , . Thus, .
Step 3: Calculation
.
.
mm.
Final Answer: (d)

Step 1: Analyze the system of blocks.
We have three blocks connected by strings. Since the surface is frictionless, we can use Newton’s second law to determine the tension in the strings. Let be the tension between and , and be the tension between and . The total force applied is , which is pulling the system forward. The blocks will experience accelerations due to this force, and we need to find the tension in the middle string, .

Step 2: Apply Newton’s second law.
The total mass of the system is: The acceleration of the system is: Now, consider the forces acting on the second block . The forces are acting to the right and acting to the left. The net force on is: Substitute and :

Step 3: Calculate the tension .
Next, we calculate the forces acting on . The only force on is the tension , so: Thus, the tension .

Step 4: Conclusion.
The tension is 32 N, which is option (4).

Step 1: Understanding the Concept:
Mirror formula: . Magnification . Differentiate w.r.t time.
Step 2: Detailed Explanation:
. Differentiating: .
.
Thus, ratio of object speed to image speed = .
Step 3: Final Answer:
Thus, ratio = .

Concept: From Newton’s second law:

Step 1: Find masses.


Step 2: Total mass.


Step 3: Acceleration of system.

Concept: Net force acting downward:

Step 1: Weight of fireman

Step 2: Net force (downward)

Step 3: Acceleration Final:

Concept: Friction provides acceleration to the lower block. At limiting condition: Also, acceleration:

Step 1: Find coefficient of friction.
When 12 N is applied on A (mass 4 kg), it just slips: Friction force:

Step 2: Maximum force for no slipping.
Total mass: Acceleration: Friction needed to move A: For no slipping:

Step 3: Solve for F.