Physics · Work, Energy And Power · NEET
Yes. Both work and energy have the SI unit joule (J) and the same dimensions [ML2T-2]. This is because work is the transfer of energy. When you do 5 J of work on a body, you give it 5 J of energy. NCERT states clearly that work and energy have the same dimensions.
Start from W = F d. In SI: 1 J = 1 newton x 1 metre = (1 kg x 1 m/s^2) x 1 m. In CGS: 1 erg = 1 dyne x 1 cm = (1 g x 1 cm/s^2) x 1 cm. Now 1 N = 10^5 dyne and 1 m = 10^2 cm, so 1 J = 10^5 dyne x 10^2 cm = 10^7 dyne cm = 10^7 erg.
Work W = force x displacement. Force has dimensions [MLT-2] (mass x acceleration). Displacement has dimension [L]. So work = [MLT-2] x [L] = [ML2T-2]. There is no charge or temperature term, so the formula only uses M, L, and T.
No. Both work and torque have dimensions [ML2T-2] and can both be written in newton metre, but they are different. Work is a scalar (W = F d cos theta, a dot product) and its SI unit is written as joule. Torque is a vector (tau = r F sin theta, a cross product) and its unit is left as newton metre, not joule, to avoid confusion. Same dimensions does not mean same physical quantity.
Numerically yes: 1 J = 1 N m. For work and energy we write joule. But newton metre is also used for torque, where we deliberately do not call it joule. So joule = newton metre only in the context of work and energy.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The SI unit of work is the joule (J), named after James Prescott Joule. One joule is the work done when a force of 1 newton moves a body through 1 metre in the direction of the force, so 1 J = 1 N m.
The CGS unit of work is the erg. One erg is the work done when a force of 1 dyne moves a body through 1 centimetre. The relation to SI is 1 joule = 10^7 erg.
The dimensional formula of work is [M1 L2 T-2], usually written [ML2T-2]. It comes from work = force x displacement = [MLT-2] x [L].
Energy, heat, torque (moment of force), and kinetic and potential energy all have dimensions [ML2T-2]. NEET often tests this list, so remember them together.
There are 10^7 (ten million) ergs in one joule, because 1 N = 10^5 dyne and 1 m = 10^2 cm, giving 1 J = 10^5 x 10^2 = 10^7 erg.
