Physics · Dawn of Modern Physics
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If ‘m’ is the mass, ‘c’ is the velocity of light and x = mc2, then dimensions of ‘x’ will be:
- A
[LT-1]
- B
[ML2T-2]
- C
[MLT-1]
- D
[MLT-2]
The equation x = mc² represents the relationship between mass and energy, where x is the energy equivalent of a mass m, and c is the speed of light.
To determine the dimensions of x, we need to consider the dimensions of each variable in the equation. The dimensions of mass are [M], the dimensions of the speed of light are [LT-1].
Using the rules of dimensional analysis, we can find the dimensions of x by substituting the dimensions of m and c into the equation and simplifying:
x = mc²
= [M][LT-1]²
= [M][L2T-2]
Therefore, the dimensions of x are [ML2T-2], which is option B.
This option is incorrect because the dimensions of x = mc2 are not [LT-1]. The dimension [LT-1] represents inverse time, which is not applicable here.
The equation x = mc² represents the relationship between mass and energy, where x is the energy equivalent of a mass m, and c is the speed of light.
To determine the dimensions of x, we need to consider the dimensions of each variable in the equation. The dimensions of mass are [M], the dimensions of the speed of light are [LT-1].
Using the rules of dimensional analysis, we can find the dimensions of x by substituting the dimensions of m and c into the equation and simplifying:
x = mc²
= [M][LT-1]²
= [M][L2T-2]
Therefore, the dimensions of x are [ML2T-2], which is option B.
This option is incorrect because the dimensions of x = mc2 are not [MLT-1]. The dimension [MLT-1] represents momentum per unit time, which is not the correct dimension for x = mc2.
This option is incorrect because the dimensions of x = mc2 are not [MLT-2]. The dimension [MLT-2] represents force per unit area, which is not relevant to the expression x = mc2.
Tagged under Physics · Dawn of Modern Physics · 2012