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Physics Question on work, energy and power

A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U (x) versus x will be (where U is the potential energy function)

A

B

C

D

Answer

Explanation

Solution

From F=−dUdxF=-\frac{dU}{dx}
∫0U(x)dU=−∫0xFdx=−∫0x(kx)dx\int_0^{U(x)}dU=-\int_0^x Fdx=-\int_0^x(kx)dx
∴   U(x)=−kx22\therefore \, \, \, U(x)=-\frac{kx^2}{2} as U (0)= 0
Therefore, the correct option is (a).