Answer:
The value is 
Explanation:
From the question we are told that
The period of the asteroid is 
Generally the average distance of the asteroid from the sun is mathematically represented as
![R = \sqrt[3]{ \frac{G M * T^2 }{4 \pi} }](https://tex.z-dn.net/?f=R%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7BG%20M%20%2A%20T%5E2%20%7D%7B4%20%5Cpi%7D%20%7D)
Here M is the mass of the sun with a value

G is the gravitational constant with value 
![R = \sqrt[3]{ \frac{6.67 *10^{-11} * 1.99*10^{30} * [5.55 *10^{9}]^2 }{4 * 3.142 } }](https://tex.z-dn.net/?f=R%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B6.67%20%2A10%5E%7B-11%7D%20%20%2A%201.99%2A10%5E%7B30%7D%20%2A%20%5B5.55%20%2A10%5E%7B9%7D%5D%5E2%20%7D%7B4%20%2A%203.142%20%7D%20%7D)
=> 
Generally

So

=> 
=> 
Solution :
Given data :
Mass of the merry-go-round, m= 1640 kg
Radius of the merry-go-round, r = 7.50 m
Angular speed,
rev/sec
rad/sec
= 5.89 rad/sec
Therefore, force required,

= 427126.9 N
Thus, the net work done for the acceleration is given by :
W = F x r
= 427126.9 x 7.5
= 3,203,451.75 J
Answer:
<h2>0.069 N, in the X direction</h2>
Explanation:
According to Flemming's left hand rule, it sates that if the first three fingers of the left hand are held mutually at right angles to one another, the fore finger will point in the direction of magnetic field, the middle finger will point in direction of current, while the thumb will point to the direction of force.
Mathematically the law is stated as
F= BIL
given data
Magnetic field B= 0.43T
Current I= 4.9 A
length of conductor L= 3.3cm to meter , 3.3/100= 0.033 m
Applying the formula the force is calculated as
F= 0.43*4.9* 0.033= 0.069 N
According to Flemming's rule the direction of all parameters are mutually perpendicular to one another, then the Force is in the X direction
Answer: 3.75 joules
Explanation:
Given that:
Mass of acorn = 0.300 kilograms
velocity = 5.oo m/s
Kinetic energy = ?
Since, kinetic energy is the energy possessed by a moving object, its value depends on the mass M and velocity V of the acorn.
Thus, Kinetic energy = 1/2 x mv^2
= 1/2 x 0.300kg x (5.00m/s)^2
= 0.5 x 0.3kg x (5.00m/s)^2
= 0.15 x (5.00m/s)^2
= 3.75 joules
Thus, the kinetic energy of the falling acorn is 3.75 joules