Center of MassHardBloom L3
Question
A sector cut from a uniform disk of radius 12 cm and a uniform rod of the same mass bent into shape of an arc are arranged facing each other as shown in the figure. If center of mass of the combination is at the origin, what is the radius of the arc?
Options
A.8 cm
B.9 cm
C.12 cm
D.18 cm
Solution
Sol. 
$x_{2} = \frac{2R_{2}}{\theta}\sin\frac{\theta}{2}$, $x_{1} = \frac{4R_{1}}{3\theta}\sin\frac{\theta}{2}$
m1x1 = m2x2 ⇒ m. $\frac{4R_{1}}{3\theta}\sin\frac{\pi}{2} = m.\frac{2R_{2}}{\theta}\sin\frac{\theta}{2}$
⇒ $R_{1} = \frac{3R_{2}}{2} \Rightarrow R_{2} = \frac{2R_{1}}{3}$
⇒ R2 = 2 × $\frac{12}{3}$ = 8 cm
Create a free account to view solution
View Solution FreeMore Center of Mass Questions
A thin uniform wire is bent to form the two equal sides AB and AC of triangle ABC, where AB = AC = 5 cm. The third side ...The fig. shows a string of equally spaced beads of mass m, separated by distance d. The beads are free to slide without ...There are two particles of same mass. If one of the particles is at rest always and the other has an acceleration . Than...A thin uniform circular disc of radius a is placed in XY plane with its center at origin (0, 0). A small circular disc o...Choose the correct statement:(1) Centre of gravity (C.G) of a body is the point at which the weigth of the body acts(2) ...