SATHEE: Gravitation Question 364

Gravitation Question 364

Question: The gravitational field in a region is given by $[\vec{g} = 5 N / k g \hat{i} + 12 N / k g \hat{j}]$ . The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point $[(7 m, - 3 m)]$ is:

Options:

A) $[71 J]$

B) $[13 \sqrt{58} J]$

C) $[- 71 J]$

D) $[1 J]$

Show Answer

Answer:

Correct Answer: D

Solution:

Gravitational field, $[I = (5 \hat{i} + 12 \hat{j}) N / k g]$

$[I = \frac{d v}{d r}]$

$[v = - [\int_{0}^{x} I_{x} d x + \int_{0}^{y} I_{y} d y] = - [I_{x} . x + I_{y} . y]]$

$[= - [5 (7 - 0) + 12 (- 3 - 0)]]$

$[= - [35 + (- 36)] = 1 J / k g]$

i.e., change in gravitational potential 1 J/kg. Hence change in gravitational potential energy 1J

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Gravitation Question 364

Question: The gravitational field in a region is given by[g→=5N/kgi^+12N/kgj^] . The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point [(7m,−3m)] is:

Options:

Answer:

Solution:

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Question: The gravitational field in a region is given by $[\vec{g} = 5 N / k g \hat{i} + 12 N / k g \hat{j}]$ . The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point $[(7 m, - 3 m)]$ is: