Question

Find the moments of inertia for lamina below d is bounded

Answer 1

Find the moments of inertia Ix, Iy, Io, for the lamina below. D is bounded by y = e^x, y = O, x = 1; and x = .1; p(x,y) = 17 y Ix= Iy= Io= A lamina with constant density p(x, y) = p occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration Bar x and Bar y. The region under the curve y = sin(x) from x = O to x = Pi. Ix= Iy= Bar X = Bar y =

Answer 2

# Given-

m = 1.7×10-27 kg

r = 4×10^-10 m

# Solution-

Here,

Total mass M = 2m

Radius of rotation R = r/2

Moment of inertia of hydrogen molecule is given by-

M.I. = MR^2

M.I. = (2m)(r/2)^2

M.I. = mr^2/2

M.I. = 1.7×10-27 × (4×10^-10)^2 / 2

M.I. = 1.36×10^-46 kgm^2