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From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is: 37 9 M R 2. 4MR 2. 40 9 M R 2. 10 MR 2

10.28 Three identical rods of length L, mass m, and radius r are placed perpendicular to each other as shown in Figure P10.22. The setup is rotated about an axis that passes through the end of one rod and is parallel to another. Determine the moment of inertia of this arrangement.
8. A horizontal piping system that delivers a constant flow of water is constructed from pipes with different diameters as shown in the figure. 2. A molecule of mass m travelling horizontally with velocity u hits a vertical wall at right angles to its velocity.
• Problem Set due Thursday, noon. A pendulum is made of a rod of length L=1 m and mass mrod =3 kg, attached to a solid sphere of radius A ball of mass m is connected to two rubber bands of length L, each under tension T as shown in the figure. the ball is...
The solid part of the sphere has a uniform volume charge density $\rho$. Find the magnitude and direction of the electric field We can see that there is a cancellation happening. So this term councils this turn and we end up with an electric field that is even...
A heavy particle of mass m, oscillates through 1800 inside of a smooth hemisphere of radius R as shown. A uniform body of mass M and radius R has a small mass m attached at edge as shown in the figure. A ball of mass 1 kg strikes a wedge of mass 4 kg horizontally with a velocity of 10 m/s.
(b) Material is removed from the sphere leaving center E 3P0 a spherical cavity that has a radius b R>2 and its center at x b on the x axis (Figure 22-46). Calculate the electric field at points 1 ...
First things first , Solid sphere - Moment of Inertia $I = 2/5MR^2$ Now the sphere is rolling on a rough horizontal surface. It means that we have some frictional forces in play.
Dec 29, 2020 · A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine: (i) The area of the sheet required for making the box. (ii) The cost of sheet for it, if a sheet measuring 1 m 2 costs Rs 20. Answer:
ω max 2 = M 2 g R/I = 4M 2 g/[(2M 1 + M 2)R]. Problem: A dumbbell consists of two spheres A and B, each with volume V, which are connected by a rigid rod. A has mass M and B has mass 2M. The distance between the centers of the spheres is d as shown below.
For θ = 0, s = R - r and s = r + R for θ = π. Using the area density expression σ = M/4πR 2, the integral can be written. Now the parts are evaluated as polynomial integrals and simplified. The net gravitational force on a point mass inside a spherical shell of mass is identically zero!
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• May 11, 2016 · 4. (40 points total) A positively charged particle with mass M and charge +e moves in a circular orbit with radius R in a uniform magnetic field directed perpendicular to the page. The figure shows the direction of the particle’s motion (in the plane of the page) at a particular instant in time.
• theorem. Looking up the moments of inertia of a flat solid disk and a thin cylindrical shell, we have Itotal = 2×½Mlidr 2 + Mshellr 2 = 4.86 × 10­5 kg­m2. 3. A dumbbell consists of two uniform spheres of mass M and radius R joined by a thin rod of mass m, length L, and radius r (see diagram).
• Sometimes a sphere comes up, so this is another common example, say you had a sphere, also rotating around an axis, like the earth rotating on its axis, and let's say it also has a mass m and a radius r.
• Given that a sphere can be thought of as a collection of infinitesimally thin, concentric, spherical shells (like the layers of an onion), then it can be shown that a corollary of the Shell Theorem is that the force exerted in an object inside of a solid sphere is only dependent on the mass of the sphere inside of the radius at which the object is.
• Apr 13, 2009 · Consider one such shell with radius r. So. volume of the spherical shell = 4πr^2 dr. Amount of charge on this shell. dq = volume*charge density = 4πr^2 ρ1 (r/R) dr. Integrate from r = 0 to r = R: Q = π(ρ1)(R^3) b) Let the electric field at a distance r from the center be E. Consider a Gaussian Surface t o be a sphere of radius r.

ω max 2 = M 2 g R/I = 4M 2 g/[(2M 1 + M 2)R]. Problem: A dumbbell consists of two spheres A and B, each with volume V, which are connected by a rigid rod. A has mass M and B has mass 2M. The distance between the centers of the spheres is d as shown below.

4-3 Figure 4.2.1 A spherical Gaussian surface enclosing a charge Q . In spherical As shown in Figure 4.2.4, the solid angle subtended is the same for both ∆A1 and ∆A2n : ∆A1 ∆ The magnitude of the electric field is constant on cylindrical surfaces of radius r...
Thus, this profile has only one free parameter, R DM. In Figure we show the total and DM mass density profiles for R DM =0.5kpc and 3kpc. In both cases we see that the total mass density profile is dominated by the stellar component within the central 4kpc. 10. Three cylinders, all of mass M, roll without slipping down an inclined plane of height H. The cylinders are described as follows: I. hollow of radius R II. solid of radius R/2 III. solid of radius R If all cylinders are released simultaneously from the same height, the cylinder (or cylinders) reaching the bottom first is (are):

Mar 13, 2018 · A sphere of radius r and mass m is placed on a horizontal floor with no linear velocity but with a clockwise angular velocity ω 0 . Denoting by µk the coefficient of kinetic friction between the sphere and the floor, determine (a) the time...

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The easiest way I know to do such questions is this: First you will need to find the linear velocity of the centre of mass of the cylinder after it starts pure rolling (call it $u$) This can be found by conserving Angular Momentum abo...