Dimensions Of Physical Quantities

Step 1: Dimension analysis.
The force is given by: The dimensions of force are [MLT ].

Step 2: Dimension of .
For the term to have dimensions of force, the dimension of must be [MLT ].

Step 3: Dimension of .
For the term to have dimensions of force, the dimension of must be [MLT ]. Thus, the correct answer is (2).

Step 1: Define scalar and vector quantities
- Scalar: Has only magnitude (e.g., mass, temperature).
- Vector: Has magnitude and direction (e.g., velocity, force).

Step 2: Analyze each option
- Velocity: Has magnitude (speed) and direction (e.g., 20 m/s north). Vector.
- Force: Has magnitude (e.g., 10 N) and direction (e.g., upward). Vector.
- Temperature: Has magnitude (e.g., 25°C) but no direction. Scalar.
- Displacement: Has magnitude (e.g., 5 m) and direction (e.g., east). Vector.

Step 3: Conclusion
Temperature is the only scalar quantity, matching option (3).

Step 1: Understanding the Question:
We need to calculate the actual diameter of a bob using Vernier caliper readings, accounting for a positive zero error.

Step 2: Key Formula or Approach:
1. Least Count (LC) = 0.1 mm = 0.01 cm.
2. Zero Error (ZE) = [since zero is to the right].
3. Observed Reading = Main Scale Reading (MSR) + (Vernier Scale Reading (VSR) LC).
4. Actual Reading = Observed Reading - Zero Error.

Step 3: Detailed Explanation:
Part 1: Calculate Zero Error
The zero of Vernier is to the right, so it's a positive zero error.
ZE = .
Part 2: Calculate Observed Reading
MSR = 3.2 cm (since zero lies between 3.2 and 3.3).
VSR = 4.
Observed Reading = .
Part 3: Calculate Actual Diameter
Actual Diameter = .

Step 4: Final Answer:
The diameter of the bob is 3.18 cm.