A particle A having a charge of 2×10^-6 Coulomb and a mass of 100g is fixed at the bottom of a smooth inclined plane of inclination 30 degree. Where should another particle B having same charge and mass, be placed on the inclined plane so that B may remain in equilibrium?
(a) 8cm from the bottom
(b) 13cm from the bottom
(c) 21cm from the bottom
(d) 27cm from the bottom
Please help me
To determine where particle B should be placed on the inclined plane so that it remains in equilibrium, we need to consider the forces acting on particle B.
The gravitational force acting on particle B is given by the equation:
F_gravity = mass * acceleration due to gravity = m * g
The Coulomb force between particles A and B is given by the equation:
F_coulomb = (k * charge_A * charge_B) / (distance^2)
In equilibrium, the net force acting on particle B should be zero. Therefore, we can set up the equation:
F_gravity = F_coulomb
Let's calculate the gravitational force acting on particle B:
F_gravity = mass * acceleration due to gravity = (0.1 kg) * (9.8 m/s^2) = 0.98 N
The Coulomb force between particles A and B is calculated using the equation:
F_coulomb = (k * charge_A * charge_B) / (distance^2)
Where:
k : is the electrostatic constant = 9 * 10^9 N * m^2 / C^2
charge_A : charge of particle A = 2 * 10^-6 C
charge_B : charge of particle B = 2 * 10^-6 C
distance : distance between particles A and B
Now, we can substitute these values into the equation to find the distance (d) at which B should be placed:
0.98 = (9 * 10^9 * 2 * 10^-6 * 2 * 10^-6) / (d^2)
Simplifying the equation gives:
0.98 * d^2 = 9 * 10^9 * 4 * 10^-12
d^2 = (9 * 10^9 * 4 * 10^-12) / 0.98
d^2 = 3.673469 * 10^-11
d ≈ √(3.673469 * 10^-11)
d ≈ 6.0685 * 10^-6
Since the question asks for the distance in centimeters, we need to convert the answer to centimeters:
d ≈ 6.0685 * 10^-6 * 100
d ≈ 6.0685 * 10^-4 cm
Based on the calculation, particle B should be placed approximately 6.0685 * 10^-4 cm from the bottom of the inclined plane.
None of the given answer options match the calculated value, so none of them is correct.