Answer:
T = 3.23 s
Explanation:
In the simple harmonic movement of a spring with a mass the angular velocity is given by
w = √ K / m
With the initial data let's look for the ratio k / m
The angular velocity is related to the frequency and period
w = 2π f = 2π / T
2π / T = √ k / m
k₀ / m₀ = (2π / T)²
k₀ / m₀ = (2π / 3.0)²
k₀ / m₀ = 4.3865
The period on the new planet is
2π / T = √ k / m
T = 2π √ m / k
In this case the amounts are
m = 6 m₀
k = 10 k₀
We replace
T = 2π√6m₀ / 10k₀
T = 2π √6/10 √m₀ / k₀
T = 2π √ 0.6 √1 / 4.3865
T = 3.23 s
Refer to the diagram shown below.
The basket is represented by a weightless rigid beam of length 0.78 m.
The x-coordinate is measured from the left end of the basket.
The mass at x=0 is 2*0.55 = 1.1 kg.
The weight acting at x = 0 is W₁ = 1.1*9.8 = 10.78 N
The mass near the right end is 1.8 kg.
Its weight is W₂ = 1.8*9.8 = 17.64 N
The fulcrum is in the middle of the basket, therefore its location is
x = 0.78/2 = 0.39 m.
For equilibrium, the sum of moments about the fulcrum is zero.
Therefore
(10.78 N)*(0.39 m) - (17.64 N)*(x-0.39 m) = 0
4.2042 - 17.64x + 6.8796 = 0
-17.64x = -11.0838
x = 0.6283 m
Answer: 0.63 m from the left end.
The work W done by the electric field in moving the proton is equal to the difference in electric potential energy of the proton between its initial location and its final location, therefore:

where q is the charge of the proton,

, with

being the elementary charge, and

and

are the initial and final voltage.
Substituting, we get (in electronvolts):

and in Joule:
Answer:

Explanation: Weight of space probes on earth is given by:
W= weight of the object( in N)
m= mass of the object (in kg)
g=acceleration due to gravity(9.81
)
Therefore,


Similarly,


Now, considering these two parts as uniform spherical objects
Also, according to Superposition principle, gravitational net force experienced by an object is sum of all individual forces on the object.
Force between these two objects is given by:

G= gravitational constant (
)
= masses of the object
R= distance between their centres (in m)(18 m)
Substituiting all these values into the above formula

This is the magnitude of force experienced by each part in the direction towards the other part, i.e the gravitational force is attractive in nature.