Physics · Dawn of Modern Physics

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.