Two initially uncharged identical metal spheres are connected by an insulating spring (unstretched length 0.75 m).Charge +2q is placed on the first sphere and -q on the second sphere,causing the spring to contract to a length of 0.54 m.Recall that the force exerted by a spring is k$\Delta$x,where $\Delta$x is the change in the spring's length from its unstretched/uncompressed length and k is the spring constant.If the charge q = 2.06 * 10^-5 C,what is the spring constant? A)125 N/m B)187 N/m C)35.0 N/m D)58.3 N/m E)142 N/m

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The force exerted by the spring is equal to the electrostatic force between the charges. The electrostatic force is given by Coulomb's law:$$F = k\frac{q_1q_2}{d^2}$$where k is Coulomb's constant, q1 and q2 are the charges, and d is the distance between the charges.The force exerted by the spring is given by:$$F = k\Delta x$$where k is the spring constant and Δx is the change in the spring's length.Setting these two forces equal to each other, we get:$$k\frac{q_1q_2}{d^2} = k\Delta x$$Solving for k, we get:$$k = \frac{q_1q_2}{d^2\Delta x}$$Plugging in the given values, we get:$$k = \frac{(2.06 	imes 10^{-5} C)^2}{(0.21 m)^2(0.54 m - 0.75 m)} = 125 N/m$$

Two Initially Uncharged Identical Metal Spheres Are Connected by an Insulating