A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation v=10 √x m / s the force acting on the body is:-

Solution

Physics sir · 4 steps

Velocity is given as a function of x, so find acceleration with a = vdv/dx, not dv/dt.

1. Square the relation. From v = 10√x you get v² = 100x. This form is the easiest to differentiate with respect to x.

   a = vdv/dx = 1/2d(v²)/dx = 1/2 × 100 = 50 m s⁻²

2. Check directly. dv/dx = 5/√x, so vdv/dx = 10√x × 5/√x = 50 m s⁻². The x cancels, so the acceleration is constant.
3. Apply F = ma. Convert the mass: 500 g = 0.5 kg. Then F = 0.5 × 50 = 25 N.
4. So. The force on the body is a constant 25 N, option (c).

The idea to keep. Whenever velocity is given in terms of position, use a = vdv/dx. If v² is linear in x, the acceleration is constant: half the coefficient of x in v².

Answer from the NTA final answer key. Solution by PrepWiser.