Question

The gravitational potential in a region is given by V = 20 N kg−1 (x + y). (a) Show that the equation is dimensionally correct. (b) Find the gravitational field at the point (x, y). Leave your answer in terms of the unit vectors→i, →j, →k. (c) Calculate the magnitude of the gravitational force on a particle of mass 500 g placed at the origin.

Answer 1

Answer:

Gravitational field is given as

$E = - 20 \hat i - 20 \hat j$

Force on the mass is 14.14 N

Explanation:

Part a)

As we know that gravitational potential is given as

$V = 20 \frac{N}{Kg} (x + y)$

so here since position x,y is measured in meter

so we have dimensions given as

$V = \frac{N \times m}{kg}$

$V = \frac{J}{Kg}$

so the dimensions are correct

Part b)

As we know that field and potential are related to each other as

$E = - \frac{dV}{dx} \hat i - \frac{dV}{dy} \hat j$

$E = - 20 \hat i - 20 \hat j$

now gravitational force on given mass is

$F = m E$

$F = 0.500( - 20 \hat i - 20 \hat j)$

$F =(0.500) 20 \sqrt 2$

$F = 14.14 N$

#Learn

Topic : Gravitational field and potential

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