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  4. The gravitational intensity in a region is 10( hati- hatj)N/kg. The work done by the gravitational force to shift slowly a particle of mass 1 Kg from point (Im, Im) to a point (2m, -2m) is

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Q. The gravitational intensity in a region is $10(\hat{i}-\hat{j})N/kg.$ The work done by the gravitational force to shift slowly a particle of mass 1 Kg from point (Im, Im) to a point (2m, -2m) is

Gravitation

Solution:

$F_g = m \overrightarrow{E_g} = 1(10 (\hat{i} - \hat{j})) = 10 (\hat{i} -\hat{j}) N = 10 \hat{i} - 10\hat{j}$
$\bar{S} = (2\hat{i} - 2\hat{j}) - ( \hat{i} - \hat{j}) = \hat{i} - 3 \hat{j} m$
Work done = $\overrightarrow{F_g} .\overrightarrow{S} = (10 \hat{i} - 10 \hat{j} ).(\hat{i} - 3 \hat{j} )$
= 10(1) + (-10)(-3)