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)

Question

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) (A) 20 N/kg (B) 13 N/kg (C) 12 N/kg (D) 5 N/kg

Tardigrade Admin · Accepted Answer

V = 3x + 4y + 12z I = -( partial V/ partial x) hati - ( partial V/ partial y) hatj - ( partial V/ partial z) hatk hatI =â3 hatiâ4 hatjâ12 hatk ∴ I = √ 9+16+144 =√169 = 13 N/kg

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)

20 N/kg

13 N/kg

12 N/kg

5 N/kg

$V = 3 x + 4 y + 12 z$
$I = - \frac{\partial V}{\partial x} \hat{i} - \frac{\partial V}{\partial y} \hat{j} - \frac{\partial V}{\partial z} \hat{k}$
$\hat{I} = - 3 \hat{i} - 4 \hat{j} - 12 \hat{k}$
$∴ I = 9 + 16 + 144 = 169 = 13 N / k g$

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)

20 N/kg

13 N/kg

12 N/kg

5 N/kg

V=3x+4y+12z I=−∂x∂V​i^−∂y∂V​j^​−∂z∂V​k^ I^=−3i^−4j^​−12k^ ∴I=9+16+144​=169​=13N/kg

$V = 3 x + 4 y + 12 z$
$I = - \frac{\partial V}{\partial x} \hat{i} - \frac{\partial V}{\partial y} \hat{j} - \frac{\partial V}{\partial z} \hat{k}$
$\hat{I} = - 3 \hat{i} - 4 \hat{j} - 12 \hat{k}$
$∴ I = 9 + 16 + 144 = 169 = 13 N / k g$