wave function of a particle with mass m is given by ψ(x)={ Acosαx −
π
2α
≤x≤+
π
2α
0 otherwise , where α=1.00×1010/m.
(a) Find the normalization constant.
(b) Find the probability that the particle can be found on the interval 0≤x≤0.5×10−10m.
(c) Find the particle’s average position.
(d) Find its average momentum.
(e) Find its average kinetic energy −0.5×10−10m≤x≤+0.5×10−10m.
Explanation:
According to Newton's second law of motion, the rate of change of momentum is directly proportional to the applied unbalanced force. The mathematical expression is given by:

Where
F is the applied force
m is the mass of the object
v is the velocity with which it is moving

Momentum of a particle is given by the product of mass and velocity as :

Hence, this is the required solution.
Answer:
Frictional force increases with the increase in the roughness of the surface.
Explanation:
You will see that the rougher the surface, the greater the wear and tear.
The sun’s gravitational attraction and the planet’s inertia keeps planets moving is circular orbits.
Explanation:
The planets in the Solar System move around the Sun in a circular orbit. This motion can be explained as a combination of two effects:
1) The gravitational attraction of the Sun. The Sun exerts a force of gravitational attraction on every planet. This force is directed towards the Sun, and its magnitude is

where
G is the gravitational constant
M is the mass of the Sun
m is the mass of the planet
r is the distance between the Sun and the planet
This force acts as centripetal force, continuously "pulling" the planet towards the centre of its circular orbit.
2) The inertia of the planet. In fact, according to Newton's first law, an object in motion at constant velocity will continue moving at its velocity, unless acted upon an external unbalanced force. Therefore, the planet tends to continue its motion in a straight line (tangential to the circular orbit), however it turns in a circle due to the presence of the gravitational attraction of the Sun.
Learn more about gravity:
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