Mass is best given by _______

Subtraction of mass and density

The body is sometimes acted by two or three force members. The difference between the two and the three force members is ___

The former is acting on two points in the body while the latter is on three points

The former is collinear and the latter is parallel

The former is parallel and the latter is perpendicular

The former is perpendicular and the latter is collinear

How to Find Centre of Mass of Hollow Hemisphere

Centre of the mass of the body is the single point at which the entire mass of the body is imagined to be concentrated and all the forces applied act at that point.

The centre of mass is that point that moves when external forces are applied to the body. The centre of mass will have a translational motion under the influence of forces.

How to Find Centre of Mass of Hollow Hemisphere

Centre of mass of hollow hemisphere

We are having a hollow hemisphere of mass M and radius R. The centre of mass of the hollow hemisphere will lie on the y-axis, which is the line passing through the centre of the base of the hollow hemisphere.

We are considering an elemental strip of width Rdθ and has a mass dM. The radius of the elemental ring is r = Rsinθ.

The elemental mass dM = (M/2πR²) (2πRsinθ.Rdθ)

dM = Msinθdθ

The y-coordinate of the centre of mass y_c =(1/M)∫ydM

Putting the values of y and dM, we get

y_c =(1/M)∫(Rcosθ)(Msinθdθ)

\(\begin{array}{l}y_{c}=\frac{1}{M}\int_{0}^{\pi /2}(Rcos\theta )(Msin\theta d\theta )\end{array} \)

\(\begin{array}{l}y_{c}=\frac{1}{M}\int_{0}^{\pi /2}(Rcos\theta )(Msin\theta d\theta ) \times \frac{2}{2}\end{array} \)

\(\begin{array}{l}y_{c}=\frac{R}{2}\int_{0}^{\pi /2}(sin2\theta d\theta )\end{array} \)

= R/2(½ + ½) = R/2

Therefore, the centre of mass of a hollow hemisphere will be at R/2 along the y-axis. Here R is the radius of the hollow hemisphere.

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Centre of Mass of Hollow Hemisphere

How to Find Centre of Mass of Hollow Hemisphere

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