Answer:
Net charge inside the cube is 321.6 C
Explanation:
Given charge density function is ρ =
side of cube is 2m
According to the definition of volume charge density total charge is given by
q = total charge = where dv = dxdydz is the volume element
on substututing the respected values we get
q =
on solving the above integration we get
q = x
x
⇒ q = 321.6 C
Therefore net charge inside the cube is 321.6 C
Answer:
The loss in rotational kinetic energy due to the collision is 36.585 J.
Explanation:
Given;
mass of the disk, m₁ = 1.64 kg
radius of the disk, r = 0. 61 m
angular velocity of the disk, ω₁ = 17.6 rad/s
mass of the rod, m₂ = 1.51 kg
length of the rod, L = 1.79 m
angular velocity of the rod, ω₂ = 5.12 rad/s (clock-wise)
let the counter-clockwise be the positive direction
let the clock-wise be the negative direction
The common final velocity of the two systems after the collision is calculated by applying principle of conservation of angular momentum ;
m₁ω₁ + m₂ω₂ = ωf(m₁ + m₂)
where;
ωf is the common final angular velocity
1.64 x 17.6 + 1.51(-5.12) = ωf(1.64 + 1.51)
21.1328 = ωf(3.15)
ωf = 21.1328 / 3.15
ωf = 6.709 rad/s
The moment of inertia of the disk is calculated as follows;
The moment of inertia of the rod about its center is calculated as follows;
The initial rotational kinetic energy of the disk and rod;
The final rotational kinetic energy of the disk-rod system is calculated as follows;
The loss in rotational kinetic energy due to the collision is calculated as follows;
Therefore, the loss in rotational kinetic energy due to the collision is 36.585 J.
Answer:
Wavelength,
Explanation:
Given that,
Number of cycles in a spiral spring is 2.91 in every 3.67 s
The velocity of the pulse in the spring is 0.925 cm/s, v = 0.00925 m/s
To find,
Wavelength
Solution,
Number of cycles per unit time is called frequency of a wave. The frequency of the longitudinal pulse is,
The wavelength of a wave is given by :
So, the wavelength of the longitudinal pulse is 0.011 meters. Hence, this is the required solution.