Answer:
0.191 s
Explanation:
The distance from the center of the cube to the upper corner is r = d/√2.
When the cube is rotated an angle θ, the spring is stretched a distance of r sin θ. The new vertical distance from the center to the corner is r cos θ.
Sum of the torques:
∑τ = Iα
Fr cos θ = Iα
(k r sin θ) r cos θ = Iα
kr² sin θ cos θ = Iα
k (d²/2) sin θ cos θ = Iα
For a cube rotating about its center, I = ⅙ md².
k (d²/2) sin θ cos θ = ⅙ md² α
3k sin θ cos θ = mα
3/2 k sin(2θ) = mα
For small values of θ, sin θ ≈ θ.
3/2 k (2θ) = mα
α = (3k/m) θ
d²θ/dt² = (3k/m) θ
For this differential equation, the coefficient is the square of the angular frequency, ω².
ω² = 3k/m
ω = √(3k/m)
The period is:
T = 2π / ω
T = 2π √(m/(3k))
Given m = 2.50 kg and k = 900 N/m:
T = 2π √(2.50 kg / (3 × 900 N/m))
T = 0.191 s
The period is 0.191 seconds.
Answer:
a) 
b) 
Explanation:
Given:
String vibrates transversely fourth dynamic, thus n = 4
mass of the string, m = 13.7 g = 13.7 × 10⁻¹³ kg
Tension in the string, T = 8.39 N
Length of the string, L = 1.87 m
a) we know
where,
= wavelength
on substituting the values, we get
or
b) Speed of the wave (v) in the string is given as:
also,
equating both the formula for 'v' we get,
on substituting the values, we get
or
or
The
sun is a ball of hot gases containing different kinds of elements at different
cores. It has a very high temperature that radiates all throughout the Milky
Way galaxy. The sun has three main parts; photosphere, chromospheres
and corona. The outer core of a star located at the chromospheres contains
mostly of hydrogen. Inside the hydrogen is helium then carbon, oxygen, neon,
magnesium silicon and the inert gas. The photosphere is scattered by the loose electrons in the corona’s plasma.
Answer:
1.33×10⁻¹⁰ N
Explanation:
F = GMm / r²
where G is the gravitational constant,
M and m are the masses of the objects,
and r is the distance between them.
F = (6.67×10⁻¹¹ N/m²/kg²) (1000 kg) (2000 kg) / (1000 m)²
F = 1.33×10⁻¹⁰ N
The probability of finding an electron with random motion at a certain energy level (distance away from) the nucleus
