Final answer:
In physics, the dimensions of different quantities can be determined by analyzing equations. In the given equations, (a) represents force, (b) represents kinetic energy, (c) represents momentum, (d) represents work done, and (e) represents angular momentum. The dimensions of these quantities can be calculated by considering the dimensions of mass, acceleration, velocity, and radius.
Step-by-step explanation:
(a) In the equation F = ma, the left-hand side of the equation represents the force. The dimension of force is given by [F] = [m] × [a] = M × LT⁻², where [m] represents the dimension of mass and [a] represents the dimension of acceleration. Therefore, the dimension of the quantity on the left-hand side of the equation is M × LT⁻².
(b) In the equation K = 0.5mv², the left-hand side of the equation represents the kinetic energy. The dimension of kinetic energy is given by [K] = [m] × [v]² = M × (LT⁻¹)² = M × L²T⁻². Therefore, the dimension of the quantity on the left-hand side of the equation is M × L²T⁻².
(c) In the equation p = mv, the left-hand side of the equation represents the momentum. The dimension of momentum is given by [p] = [m] × [v] = M × (LT⁻¹) = MLT⁻¹. Therefore, the dimension of the quantity on the left-hand side of the equation is MLT⁻¹.
(d) In the equation W = mas, the left-hand side of the equation represents the work done. The dimension of work done is given by [W] = [m] × [a] × [s] = M × LT⁻² × L = ML²T⁻². Therefore, the dimension of the quantity on the left-hand side of the equation is ML²T⁻².
(e) In the equation L = mvr, the left-hand side of the equation represents the angular momentum. The dimension of angular momentum is given by [L] = [m] × [v] × [r] = M × (LT⁻¹) × L = ML²T⁻¹. Therefore, the dimension of the quantity on the left-hand side of the equation is ML²T⁻¹.