This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
To find the dimensions of energy, we can use the formula for work done, as energy and work have the same dimensions. Step 1: Recall the formula for work done. Work done (W) is defined as force (F) multiplied by distance (d): W = F × d Step 2: Determine the dimensions of force. Force (F) is defined as mass (m) multiplied by acceleration (a): F = m × a The dimensions of mass are M. The dimensions of acceleration are length (L) divided by time squared (T^2), so: [a] = LT^2 = L T^-2 Therefore, the dimensions of force are: [F] = [m] × [a] = M × L T^-2 = M L T^-2 Step 3: Determine the dimensions of work done (energy). Now substitute the dimensions of force and distance into the work done formula: [W] = [F] × [d] [W] = (M L T^-2) × L [W] = M L^2 T^-2 Step 4: Compare with the given options. The dimensions of energy are M L^2 T^-2. Let's check the options: (a) MLT (b) LT^2/m (which is M^-1 L T^2) (c) ML^2T^-2 (d) m^2L^3T (assuming 'm' is mass, this would be M^2L^3T) Option (c) matches our calculated dimensions. The correct combination of dimensions for energy is c) ML^2T^-2.