Question:

The gravitational field in a region is given by $\bar{E}=(4i+j)N/kg.$ Workdone this field is zero when a particle is moved along the line

Updated On: Aug 1, 2022
  • y+4 x=2
  • 4 y + x = 6
  • x + y = 5
  • all of these
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The Correct Option is A

Solution and Explanation

Workdone will be zero when displacement is perpendicular to the to .The told makes an angle $\theta_1 = \tan^{-1} \left(\frac{1}{4} \right)$ with positive x-axis. The line y + 4x = 2 makes an angle $\theta_2 = \tan^{-1} (-4)$ with positive x-axis
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Concepts Used:

Gravitational Potential Energy

The work which a body needs to do, against the force of gravity, in order to bring that body into a particular space is called Gravitational potential energy. The stored is the result of the gravitational attraction of the Earth for the object. The GPE of the massive ball of a demolition machine depends on two variables - the mass of the ball and the height to which it is raised. There is a direct relation between GPE and the mass of an object. More massive objects have greater GPE. Also, there is a direct relation between GPE and the height of an object. The higher that an object is elevated, the greater the GPE. The relationship is expressed in the following manner:

PEgrav = mass x g x height

PEgrav = m x g x h

Where,

m is the mass of the object,

h is the height of the object

g is the gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.