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Physics Question 7 – NEET-UG 2024

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The quantities which have the same dimensions as those of solid angle are :

Recall the definition and dimensional formula for solid angle.

Step 1: Determine the dimensions of solid angle✦ Active

Solid angle (Ω) is defined as the ratio of the area (A) subtended by a surface to the square of the radius (r) of the sphere. Its formula is Ω=Ar2.

Dimensions of solid angle=[L2][L2]=[M0L0T0]

Thus, solid angle is a dimensionless quantity.

Step 2: Analyze the dimensions of quantities in each option○ Expand

Let's determine the dimensions for each quantity mentioned in the options:

1. **Stress:** Force per unit area. Dimensions = [MLT−2][L2]=[ML−1T−2]. (Not dimensionless)

2. **Angle (plane angle):** Ratio of arc length to radius. Dimensions = [L][L]=[M0L0T0]. (Dimensionless)

3. **Strain:** Change in length divided by original length. Dimensions = [L][L]=[M0L0T0]. (Dimensionless)

4. **Arc:** A length. Dimensions = [L]. (Not dimensionless)

5. **Angular speed:** Angle per unit time. Dimensions = [M0L0T0][T]=[T−1]. (Not dimensionless)

💡 Teacher's Secret Hint

Remember that both plane angle and solid angle are dimensionless quantities, but they are distinct physical quantities.

Step 3: Identify the correct option○ Expand

We are looking for quantities that have the same dimensions as solid angle, which is dimensionless ([M0L0T0]).

Comparing the dimensions calculated in Step 2, both strain and angle are dimensionless quantities.

Therefore, option (4) 'strain and angle' consists of quantities that are both dimensionless, matching the dimensions of solid angle.

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