1. Tardigrade
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  3. Physics
  4. Gravitational potential in a region is given by V = (3x + 4y + 12z). The magnitude of gravitational field at (x = 1 m, y = 0 m, z = 3 m) is (where V is in J/kg and x, y and z are in m)

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Q. Gravitational potential in a region is given by V = (3x + 4y + 12z). The magnitude of gravitational field at (x = 1 m, y = 0 m, z = 3 m) is (where V is in J/kg and x, y and z are in m)

Solution:

$V = 3x + 4y + 12z$
$\overrightarrow{I} = -\frac{\partial V}{\partial x}\hat{i} - \frac{\partial V}{\partial y}\hat{j} - \frac{\partial V}{\partial z}\hat{k}$
$\hat{I} =−3\hat{i}−4\hat{j}−12\hat{k}$
$\therefore \,I = \sqrt {9+16+144} =\sqrt{169} \,=\,13\,N/kg $