Physics: A ball of radius R and mass m is magically put inside a thin shell of the same mass and radius 2R. The system is at rest on a horizontal frictionless surface initially. When the ball is, again magically, released inside the shell, it sloshes around in the shell and eventually stops at the bottom of the shell. How far does the shell move from its initial contact point with the surface

A ball of radius R and mass m is magically put

favre22fs

14.02.2022

$x =\frac{-R}{2}$

Explanation:

From the question we are told that mass

Thin layer radius = 2R

Generally the expression for ths solution is given as

Xcm =(m*0 =m(-2R))/2m =-mR/(2m)=-R/2

the center of mass will not move at initial state

Considering the center of mass of both bodies

$xcm=\frac{m*x+m*x)}{2m} =x$

$x =\frac{-R}{2}$

Therefore the enclosing layer moves $x =\frac{-R}{2}$

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lea5261

03.04.2020

25208.33

Explanation:

Thickness of the glass plate 2.50mm = 2.50 × 10⁻³m

refractive index of the glass = 1.65

wavelength of the light in vaccum = 600nm

distance between source and screen = 1.35cm = 1.35 × 10⁻²m

wavelength of light in the medium

λ = 600 × 10⁻⁹ / 1.65

λ = 3.6364 × 10⁻⁷

number of wavelength in glass

$n_1 = \frac{t}{\lambda} \\\\n_1 = \frac{2.50\times 10^-^3}{3.6364\times 10^-^7}\\ \\n_1 = 6875$

Distance travel by light in air

D = d - t

D = 1.35 × 10⁻² - 2.50 × 10⁻³

D = 0.011m

Thus, the number of wavelength

$N_2=\frac{D}{\lambda}$

$N_2 =\frac{0.011}{600\times 10^-^9} \\\\N_2 = 1833.33$

Total number of wavelength is

$N = N_1+N_2\\\\N = 6875+1833.33\\\\N = 25208.33$

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