charge must be equal to 5.74 ×10⁻⁵
In the question it is said that the particle remains stationary which means the the net force on the particle is zero. So, the counterbalancing forces must be equal which means weight is equal to upward electric force.
→ Fnet =0
→ mg = qE
substituting the values we get :
0.00345 × 9.81 = q × 590
→ q = 5.74 ×10⁻⁵
Hence the charge must be equal to 5.74 ×10⁻⁵.
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# SPJ4
The size of the force varies inversely as the square of the distance between the two charges. Therefore, if the distance between the two charges is doubled, the attraction or repulsion becomes weaker, decreasing to one-fourth of the original value.
Answer:
(a) 3107.98 J
(b) 14530.6 J
Explanation:
mass, m = 3.56 kg
angular speed, ω = 179 rad/s
Moment of inertia of solid cylinder, I = 1/2 mr^2
where, m is the mass and r be the radius of the cylinder.
(a) radius, r = 0.330 m
I = 0.5 x 3.56 x 0.330 x 0.330 = 0.194 kgm^2
The formula for the rotational kinetic energy is given by

K = 0.5 x 0.194 x 179 x 179 = 3107.98 J
(b) radius, r = 0.714 m
I = 0.5 x 3.56 x 0.714 x 0.714 = 0.907 kgm^2
The formula for the rotational kinetic energy is given by

K = 0.5 x 0.907 x 179 x 179 = 14530.6 J
Differentiate the components of position to get the corresponding components of velocity :


At <em>t</em> = 5.0 s, the particle has velocity


The speed at this time is the magnitude of the velocity :

The direction of motion at this time is the angle
that the velocity vector makes with the positive <em>x</em>-axis, such that
