Answer:
Explanation:
We know that force acting on an object due to Earth's gravity on the surface is given by:
where g is the acceleration due to gravity, r would be radius of Earth, M is the mass of Earth and G is the gravitational constant.
It is given that at pole, g = 9.830 m/s² and r = 6371 km = 6371 × 10³ m
Hence, Earth's mass is
Answer:
time taken is equal to 14,156 years
Explanation:
we know,
at t = 0
Y(0) = A
given that half life of plutonium 239 = 24,200
hence time taken is equal to 14,156 years
Quasi frequency = 4√6
Quasi period = π√6/12
t ≈ 0.4045
<u>Explanation:</u>
Given:
Mass, m = 20g
τ = 400 dyn.s/cm
k = 3920
u(0) = 2
u'(0) = 0
General differential equation:
mu" + τu' + ku = 0
Replacing the variables with the known value:
20u" + 400u' + 3920u = 0
Divide each side by 20
u" + 20u' + 196u = 0
Determining the characteristic equation by replacing y" with r², y' with r and y with 1 in the differential equation.
r² + 20r + 196 = 0
Determining the roots:
r = -10 ± 4√6i
The general solution for two complex roots are:
y = c₁ eᵃt cosbt + c₂ eᵃt sinbt
with a the real part of the roots and b be the imaginary part of the roots.
Since, a = -10 and b = 4√6
u(t) = c₁e⁻¹⁰^t cos 4√6t + c₂e⁻¹⁰^t sin 4√6t
u(0) = 2
u'(0) = 0
(b)
Quasi frequency:
μ =
(c)
Quasi period:
T = 2π / μ
(d)
|u(t)| < 0.05 cm
u(t) = |2e⁻¹⁰^t cos 4√6t + 5√6/6 e⁻¹⁰^t sin 4√6t < 0.05
solving for t:
τ = t ≈ 0.4045
Answer:
Work done to lift the box is 515.03 J
Explanation:
By work energy theorem we know that work done by all forces is equal to change in kinetic energy
So we have
so we have
so we have