The gravitational potential in a region is given by V = (3x + 4y + 12z) J/kg. The modulus of the gravitational field at (x = 1, y = 0,z = 3) is :
Answer & explanation
Correct answer: option 2
\(I = -(\frac{\delta V}{\delta x} \hat{i}+\frac{\delta V}{\delta y} \hat{j}+\frac{\delta V}{\delta z} \hat{k})\)
\(I = -(3\hat{i}+4\hat{j}+12\hat{k})\)
[As V = (3x + 4y + 12z) : given]
It is uniform field Hence its value is same every where :
\(|I| = \sqrt{3^2+4^2+12^2}\) = 13 N/kg