The force acting on a particle of mass m moving along the x-axis is given by F(x)=Ax2−Bx. Which one of the following is the potential energy of the particle?
A
2Ax−B
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B
−X26(2Ax−3B)
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C
Ax3−Bx2
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D
Zero
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Solution
The correct option is B−X26(2Ax−3B) The relation between the Force F(x) acting on a particle of mass m moving in a linear direction and the Potentional Energy U(x) is given by ;
F(x) = −dUdx............(1)
Here, F(x) = Ax2−Bx............(2),
From equation (1) and (2) and by integrating the equation (2) between the limits 0 and x. we get;