Gravtational potential varies alolngl x-axis as shown in figure .
(a) Plot E versus x graph corresponding to given `V-x` graph.
(b) A mass of 2 kg is kept at `x = 3m`. Find gravitational force on it.

Answer

B

Explanation

(a) `E = -(dV)/(dx) = -`slope of `V-x` graph.
From `x = 0` to `x = 4m`
slope `= +(10)/(4) = (2.5) N//kg`
`:. E = -(2.5) N//kg`
From `x = 4m` to `x = 8m`
Slope `= 0`
`:. E = 0`
From `x = 8m` to `x = 12m`
Slope = `-(10)/(4) = -2.5 N//kg`
`:. E = +(2.5) N//kg` Therfore, `E-x` graph is as shown in figure. (b) At `x = 3m`, `E = -2.5 N//kg`
`:.` Gravitational force
`F = mE` (as `E = (F)/(m)`)
`(2)(- 2.5) = - 5N`
Here, negative sign implies that this force is acting towards negative x-direction.