Two identical particles,each with a mass of 2.0 $\mu$g and a charge of 25 nC,are released simultaneously from rest when the two are 4.0 cm apart.What is the speed of either particle at the instant when the two are separated by 10 cm?
A)7.3 m/s
B)9.8 m/s
C)9.2 m/s
D)6.5 m/s
E)4.6 m/s

Question

Quizplus · Accepted Answer

Using conservation of energy, we can find the final speed of each particle at a separation of 10 cm.

The initial potential energy of the system is:

U_i = kq^2/r_i = (9x10^9 Nm^2/C^2)(0.025 C)^2/(0.04 m) = 1.40625 J

The final potential energy of the system is:

U_f = kq^2/r_f = (9x10^9 Nm^2/C^2)(0.025 C)^2/(0.1 m) = 0.3515625 J

The change in potential energy is:

ΔU = U_f - U_i = -1.0546875 J

This change in potential energy is equal to the kinetic energy gained by the particles:

ΔU = 1/2 mv^2

Solving for v, we get:

v = sqrt(2ΔU/m) = sqrt(2(-1.0546875 J)/(2x2x10^-6 kg)) = 6.5 m/s

Therefore, the answer is (D) 6.5 m/s.

Two Identical Particles,each with a Mass of 2 μ\muμ G and a Charge of 25 NC,are Released Simultaneously from and a Charge

Two Identical Particles,each with a Mass of 2 $\mu$ G and a Charge of 25 NC,are Released Simultaneously from and a Charge