Physics · Units And Measurements · NEET
Yes. Work is force times displacement, W = F x d = [MLT^-2] x [L] = [M L^2 T^-2]. Energy is the capacity to do work, so it must have the same dimensions [M L^2 T^-2]. Kinetic energy (1/2)mv^2 = [M][LT^-1]^2 = [M L^2 T^-2] and potential energy mgh = [M][LT^-2][L] = [M L^2 T^-2] both match. Same dimensions means the same physical nature, which is why they can be added and share the unit joule.
Power = work / time = [M L^2 T^-2] / [T] = [M L^2 T^-3]. You start with energy [M L^2 T^-2] and divide by one more factor of time, so the time exponent goes from -2 to -3. This single extra division by T is the only difference between energy and power dimensions.
Force = mass x acceleration. Mass is [M]. Acceleration is change in velocity per time = [LT^-1]/[T] = [LT^-2]. Multiply: F = [M] x [LT^-2] = [M L T^-2]. This is the base building block, because work, energy, torque and pressure are all built from force.
Energy [M L^2 T^-2] measures a total amount of work stored or transferred. Power [M L^2 T^-3] measures how fast that energy is delivered (energy per second). Power has exactly one more T^-1 than energy. If two quantities differ only by a factor of time, one is a 'rate' of the other, and this shows up as the extra T^-1.
No, they are identical: both are [M L^2 T^-2]. Kinetic energy (1/2)mv^2 uses velocity squared, and potential energy mgh uses g x h; both reduce to [M L^2 T^-2]. This is expected because all forms of energy must have the same dimensions so they can be added in the conservation of energy equation.
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities, find the dimensions of energy.
A force defined by F = alpha t + beta t^2 acts on a particle at a given time t. The factor which is dimensionless, if alpha and beta are constants, is:
If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Force = mass x acceleration = [M] x [L T^-2] = [M L T^-2]. Its SI unit is the newton (N).
Both are [M L^2 T^-2] because work = force x displacement and energy is the capacity to do work. Their SI unit is the joule (J).
Power = work / time = [M L^2 T^-2] / [T] = [M L^2 T^-3]. Its SI unit is the watt (W).
All three depend on mass through force (F = ma). Work and power are built by multiplying force by length or dividing by time, but the single mass factor [M] carries through all of them.
Yes, torque = force x perpendicular distance = [M L^2 T^-2], the same as work and energy. But torque is a vector and work is a scalar, so they are different physical quantities despite equal dimensions. This is a common NEET trap.
