Answer:
Explanation:
capacitance of sphere 2 will be 4.5 times sphere 1
a ) when spheres are in contact they will have same potential finally . So
V_1 / V_2 = 1
b )
Charge will be distributed in the ratio of their capacity
charge on sphere1 = q x 1 / ( 1 + 4.5 )
= q / 5.5
fraction = 1 / 5.5
c ) charge on sphere 2
= q x 4.5 / 5.5
fraction = 4.5 / 5.5
d ) surface charge density of sphere 1
= q /( 5.5 x A ) where A is surface area
surface charge density of sphere 2
= q x 4.5 /( 5.5 x 4.5² A ) where A is surface area
= q /( 5.5 x 4.5 A )
q_1/q_2 = 4.5
Answer:
t = 0.319 s
Explanation:
With the sudden movement of the athlete a pulse is formed that takes time to move along the rope, the speed of the rope is given by
v = √T/λ
Linear density is
λ = m / L
λ = 4/20
λ = 0.2 kg / m
The tension in the rope is equal to the athlete's weight, suppose it has a mass of m = 80 kg
T = W = mg
T = 80 9.8
T = 784 N
The pulse rate is
v = √(784 / 0.2)
v = 62.6 m / s
The time it takes to reach the hook can be searched with kinematics
v = x / t
t = x / v
t = 20 / 62.6
t = 0.319 s
Answer:
, repulsive
Explanation:
The magnitude of the electric force between two charged particles is given by Coulomb's law:
where:
is the Coulomb's constant
are the two charges of the two particles
r is the separation between the two charges
The force is:
- repulsive if the two charges have same sign
- Attractive if the two charges have opposite signs
In this problem, we have two electrons, so:
is the magnitude of the two electrons
is their separation
Substituting into the formula, we find the electric force between them:

And the force is repulsive, since the two electrons have same sign charge.
The thermal efficiency of an engine is

where
W is the work done by the engine
Q is the heat absorbed by the engine to do the work
In this problem, the work done by the engine is W=200 J, while the heat exhausted is Q=600 J, so the efficiency of the machine is