An object of mass 500 g moves along the x-axis with speed v = 4√x m/s. The magnitude of the force acting on it is:
Options

Question

An object of mass 500 g moves along the x-axis with speed v = 4√x m/s. The magnitude of the force acting on it is:

G1 Physics · Accepted Answer

Given, v = 4√x. Square both sides: v² = 16x. Differentiate with respect to x: 2v(dv/dx) = 16. Thus, v(dv/dx) = 8. But acceleration in one-dimensional motion is a = v(dv/dx). Therefore, a = 8 m/s². Mass: m = 500 g = 0.5 kg. Hence, F = ma = 0.5×8 = 4 N. Correct option: D.