The pair of quantities having the same dimensions isa. force, accelerationb. displacement, velocityc.wavelength, focal lengthd. time, frequency
Question
The pair of quantities having the same dimensions is
a. force, acceleration
b. displacement, velocity
c. wavelength, focal length
d. time, frequency
Solution
To determine the pair of quantities that have the same dimensions, we need to consider the dimensions of each option.
a. Force has dimensions of mass times acceleration (M * L / T^2), while acceleration has dimensions of length divided by time squared (L / T^2). Therefore, force and acceleration have the same dimensions.
b. Displacement has dimensions of length (L), while velocity has dimensions of length divided by time (L / T). Therefore, displacement and velocity do not have the same dimensions.
c. Wavelength has dimensions of length (L), while focal length has dimensions of length (L). Therefore, wavelength and focal length have the same dimensions.
d. Time has dimensions of time (T), while frequency has dimensions of 1 divided by time (1 / T). Therefore, time and frequency do not have the same dimensions.
Based on the analysis above, the pair of quantities that have the same dimensions is a. force, acceleration.
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