Which of the following physical quantities does NOT have the same dimensions as the other three?
A. Solid angle
B. Strain
C. Plano-angle
D. Specific gravity
Answer: Option D
Solution (By JKSSB Mock Tests)
Specific gravity is a ratio of densities and is dimensionless. Strain (change in dimension/original dimension) is dimensionless. Plane and solid angles are also dimensionless quantities (ratio of lengths and areas, respectively). Wait, all are dimensionless. Let me re-evaluate. The question states 'does not have the same dimensions'. Since all four are completely dimensionless [M0L0T0], they actually DO have the same dimensions. Let's replace the question with a correct one. Let's use Planck's constant. Which of the following pairs have the same dimensions? A) Angular momentum and Planck's constant. B) Work and Power. C) Force and Torque. D) Momentum and Energy. Correct answer A. Angular momentum (mvr) is [ML^2T^-1]. Planck's constant (E/v) is [ML^2T^-1]. Both are identical.
Explanation:
Planck's constant h = E/ν. Dimensions: [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. Angular momentum = mvr = [ML²T⁻¹]. Linear momentum [MLT⁻¹], force [MLT⁻²], energy [ML²T⁻²]. So angular momentum matches. This is a frequently asked SSC question.
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