The gravitational field in a region is given by $\to E = (5 n k g^{- 1}) \to i + (12 N k g^{- 1}) \to j$ (a) Find the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin. (b) Find the potential at the points (12 m, 0) and (0,5 m) if the potential at the origin is taken to be zero. (c) Find th echange in gravitational potential energy if a particle of mass 2 kg is taken from the origin to the point (12 m, 5m). (d) Find the change in potential energy if the particle is taken from (12 m, 0) to (0, 5 m).

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Solution

$^E = (\frac{5 N}{k g})^i + (\frac{12 N}{k g})^j$
(a) $\to F = \to E m = 2 k g [(\frac{5 N}{k g})^i + (\frac{12 N}{k g})^j] = (10 N)^i + (24 N)^j | \to F | = \sqrt{100 + 576} = \sqrt{676} = 26 N$
$(b) \to V = \to E r A t (12 m, 0), \to V = - (\frac{60 J}{k g})^i | \to V | = 60 j A t (0, 5 m), \to V = - (\frac{60 j}{k g})^j, | \to V | = - 60 J (c) △ V = \int_{(12, 0)}^{(0, 5)} E m d r [(10 N)^i + (24 N)^j r] = - (120^j^i) + (120^j^i) = 240 J (d) △ V = - [r (10 N^i + 24 N^j)] = - 120^j + 120^j = 0$

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