Answer:
a) ![R_s = 0.092](https://tex.z-dn.net/?f=R_s%20%3D%200.092)
b) ![R_p = 0.085](https://tex.z-dn.net/?f=R_p%20%3D%200.085)
Explanation:
given,
n =1.5 for glass surface
n = 1 for air
incidence angle = 45°
using Fresnel equation of reflectivity of S and P polarized light
![R_s=\left | \dfrac{n_1cos\theta_i-n_2cos\theta_t}{n_1cos\theta_i+n_2cos\theta_t} \right |^2\\R_p=\left | \dfrac{n_1cos\theta_t-n_2cos\theta_i}{n_1cos\theta_t+n_2cos\theta_i} \right |^2](https://tex.z-dn.net/?f=R_s%3D%5Cleft%20%7C%20%5Cdfrac%7Bn_1cos%5Ctheta_i-n_2cos%5Ctheta_t%7D%7Bn_1cos%5Ctheta_i%2Bn_2cos%5Ctheta_t%7D%20%5Cright%20%7C%5E2%5C%5CR_p%3D%5Cleft%20%7C%20%5Cdfrac%7Bn_1cos%5Ctheta_t-n_2cos%5Ctheta_i%7D%7Bn_1cos%5Ctheta_t%2Bn_2cos%5Ctheta_i%7D%20%5Cright%20%7C%5E2)
using snell's law to calculate θ t
![sin \theta_t = \dfrac{n_1sin\theta_i}{n_2}=\dfrac{sin45^0}{1.5}=\dfrac{\sqrt{2}}{3}](https://tex.z-dn.net/?f=sin%20%5Ctheta_t%20%3D%20%5Cdfrac%7Bn_1sin%5Ctheta_i%7D%7Bn_2%7D%3D%5Cdfrac%7Bsin45%5E0%7D%7B1.5%7D%3D%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B3%7D)
![cos \theta_t =\sqrt{1-sin^2\theta_t} = \dfrac{sqrt{7}}{3}](https://tex.z-dn.net/?f=cos%20%5Ctheta_t%20%3D%5Csqrt%7B1-sin%5E2%5Ctheta_t%7D%20%3D%20%5Cdfrac%7Bsqrt%7B7%7D%7D%7B3%7D)
a) ![R_s=\left | \dfrac{\dfrac{1}{\sqrt{2}}-\dfrac{1.5\sqrt{7}}{3}}{\dfrac{1}{\sqrt{2}}+\dfrac{1.5\sqrt{7}}{3}} \right |^2](https://tex.z-dn.net/?f=R_s%3D%5Cleft%20%7C%20%5Cdfrac%7B%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D-%5Cdfrac%7B1.5%5Csqrt%7B7%7D%7D%7B3%7D%7D%7B%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%2B%5Cdfrac%7B1.5%5Csqrt%7B7%7D%7D%7B3%7D%7D%20%5Cright%20%7C%5E2)
![R_s = 0.092](https://tex.z-dn.net/?f=R_s%20%3D%200.092)
b) ![R_p=\left | \dfrac{\dfrac{\sqrt{7}}{3}-\dfrac{1.5}{\sqrt{2}}}{\dfrac{\sqrt{7}}{3}+\dfrac{1.5}{\sqrt{2}}} \right |^2](https://tex.z-dn.net/?f=R_p%3D%5Cleft%20%7C%20%5Cdfrac%7B%5Cdfrac%7B%5Csqrt%7B7%7D%7D%7B3%7D-%5Cdfrac%7B1.5%7D%7B%5Csqrt%7B2%7D%7D%7D%7B%5Cdfrac%7B%5Csqrt%7B7%7D%7D%7B3%7D%2B%5Cdfrac%7B1.5%7D%7B%5Csqrt%7B2%7D%7D%7D%20%5Cright%20%7C%5E2)
![R_p = 0.085](https://tex.z-dn.net/?f=R_p%20%3D%200.085)
Answer:
A) Gravitational Force is greater in S.
B) Time taken to fall a given distance in air will be greater for F.
C) Both will take same time to fall in a vacuum.
D) Total force is greater in S.
Explanation:
(a) In this case, the gravitational force of S will be greater, because Newton's Second Law states that - F = ma, or weight =mg. g is constant. And mass of the solid metal is heavier.
(b) In this case, the time it will take for F to fall from a given distance in air will be greater than that of S, since the air resistance is not negligible (as in the case of S).
(c) In this, It will take same time for S and F because in a vacuum, there are no air particles, so there is no air resistance and gravity is the only force acting and so objects fall at the same rate in a vacuum.
(d) The total force will be greater in S than F because Force=ma and S is of heavier mass than F.
A hypothesis is an educated prediction that can be tested.
Answer:
The false statement is in option 'd': The center of mass of an object must lie within the object.
Explanation:
Center of mass is a theoretical point in a system of particles where the whole mass of the system is assumed to be concentrated.
Mathematically the position vector of center of mass is defined as
![\overrightarrow{r}_{com}=\int \overrightarrow{r}_{i}dm](https://tex.z-dn.net/?f=%5Coverrightarrow%7Br%7D_%7Bcom%7D%3D%5Cint%20%5Coverrightarrow%7Br%7D_%7Bi%7Ddm)
where,
is the position vector of the mass dm.
As we can see for homogenous symmetrical objects such as a sphere,cube,disc the center of mass is located at the centroid of the shapes itself but in many shapes it is located outside the body also.
Examples of shapes in which center of mass is located outside the body:
1) Horseshoe shaped body.
2) A thin ring.
In many cases we can make shapes of bodies whose center of mass lies outside the body.