Answer:
(a) 
(b) 
(c) 
Solution:
As per the question:
Mass of Earth, 
Mass of Moon, 
Mass of Sun, 
Distance between the earth and the moon, 
Distance between the earth and the sun, 
Distance between the sun and the moon, 
Now,
We know that the gravitational force between two bodies of mass m and m' separated by a distance 'r' is given y:
(1)
Now,
(a) The force exerted by the Sun on the Moon is given by eqn (1):



(b) The force exerted by the Earth on the Moon is given by eqn (1):



(c) The force exerted by the Sun on the Earth is given by eqn (1):



Let <em>F₁ </em>and <em>F₂</em> denote the two forces, and <em>R</em> the resultant force.
<em>F₁ </em>and <em>F₂</em> point perpendicularly to one another, so their dot product is
<em>F₁ </em>• <em>F₂</em> = 0
<em />
We're given that one of these vectors, say <em>F₁</em>, makes an angle with <em>R</em> of 30°, so that
<em>F₁</em> • <em>R</em> = ||<em>F₁</em>|| ||<em>R</em>|| cos(30°)
But we also have
<em>F₁</em> • <em>R</em> = <em>F₁ </em>• (<em>F₁ </em>+ <em>F₂</em>) = (<em>F₁ </em>• <em>F₁</em>) + (<em>F₁ </em>• <em>F₂</em>) = <em>F₁ </em>• <em>F₁ </em>=<em> </em>||<em>F₁</em>||²
So, knowing that ||<em>R</em>|| = 100 N, we get that
(100 N) ||<em>F₁</em>|| cos(30°) = ||<em>F₁</em>||²
(100 N) cos(30°) = ||<em>F₁</em>||
||<em>F₁</em>|| ≈ 86.6 N
(And the same would be true for <em>F₂</em>.)
Answer:
1) The angle of deflection will be less than 45° ( C )
2) The angle of deflection will be greater than 45° but less than 90° ( E )
Explanation:
1) Assuming that the force applied has a direction which is perpendicular to the Earth's magnetic field
∴ Fearth > Fapplied hence the angle of deflection will be < 45°
2) when the Fearth < Fapplied
the angle of deflection will be : > 45° but < 90°
Answer:
Explanation:
The acceleration of an object is given by the formula
a = v²/r
The acceleration of the object is bound to increase, if and only if the following are changed as well.
The mass of the object is increased,
The speed of the object is increased,
The radius of the object is contrarily decreased
Taking another look at the formula, we see that if we increase the speed of the object, it increases the acceleration. And since the radius is in the denominator, it has to be reduced for the acceleration to increase