Question

1 J Is equal to $1kgm{s^{ - 2}}$
A. true
B. false
C. ambiguous
D. data insufficient

Answer 1

When we tell two physical quantities are equal the basic requirement to be fulfilled is their dimensions must be equal. Hence in order to verify the formulas we check if they are dimensionally correct. The dimensions of the left side of the equation must be equal to dimensions of the right side of the equation.

Complete answer:
Kilogram (kg) is the unit of mass while meter(m) is unit of length and second(s) is the unit of time.
The amount of energy delivered to an object when force of 1 newton acts on the body along the direction of motion through a distance of 1 meter is called a joule.
It is the derived SI unit for energy or work.
The dimension of joule is same as dimension of work
Work = force x displacement
Units of force is newton or $kgm/{s^2}$
Unit of displacement Is meter(m).
Units of work will be $kg{m^2}/{s^2}$
Dimension of mass (kg) is M
Dimension of length (meter) is L
Dimension of time (second) is T
Hence dimensions of work = dimensions of joule
Hence dimensions of joule $(kg{m^2}/{s^2})$ is $[M{L^2}{T^{ - 2}}]$
Dimensions of $kgm/{s^2} is [ML{T^{ - 2}}]$
Both dimensions are not equal. Hence it is false

So, the correct answer is “Option B”.

Additional Information:
There are some quantities which have units but don’t have dimensions. Plane Angle is one of the examples for those types of quantities. Unit of plane angle is radian while it has no dimensions.

Note:
Joule is the unit of work or energy while $kgm/{s^2}$ is the unit of force. some physical quantities might have the same dimensional formulas while they represent different quantities. For example torque and work have the same dimensions but their purposes of serving and their usages are completely different.