Question

Gravitational potential at X= 2 m is decreasing at a rate of 10 J//kg - m along the positive x- direction. If implies that the magnitude of gravitational filed at X = 2m is also 10 n//kg. Is this statement true or false?

Answer 1

Given :

Gravitational potential energy at X=2m (dv/dx) = -10 j/kg-m      (Negative sign is due to that the gravitational potential energy is decreasing)

To find :

The magnitude of gravitational potential energy at X=2m

Solution :

• E = -[(dv/dx)i + (dv/dy)j + (dv/dz)k]
•  I E I = √[(-dv/dx)²+(-dv/dy)²+(-dv/dz)²]

• We have the value of  (dv/dx) = -10 j/kg-m,but the remaining values are not mentioned in the question above

• As the value of (dv/dx) = -10,we can say that the value of I E I should always be greater than or equal to 10

   I E I ≥10

Conclusion:

     The given statement is false