Two semicircular rings of linear mass densiti | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the mass of the semicircular ring with density $\lambda$ be $M_1 = \lambda (\pi R) = M$. Then the mass of the semicircular ring with density $

Vedclass · Accepted Answer

$\frac{ R }{\pi}$

Vedclass · Answer

(B) Let the mass of the semicircular ring with density $\lambda$ be $M_1 = \lambda (\pi R) = M$. Then the mass of the semicircular ring with density $3 \lambda$ is $M_2 = 3 \lambda (\pi R) = 3M$. The centre of mass of a semicircular ring of radius $R$ lies at a distance $\frac{2R}{\pi}$ from the centre along the axis of symmetry. Let the geometrical centre be the origin $(0,0)$. Place the first ring in the left half such that its centre of mass is at $x_1 = -\frac{2R}{\pi}$. Place the second ring in the right half such that its centre of mass is at $x_2 = \frac{2R}{\pi}$. The centre of mass of the composite system is $X_{cm} = \frac{M_1 x_1 + M_2 x_2}{M_1 + M_2}$. Substituting the values: $X_{cm} = \frac{M(-\frac{2R}{\pi}) + 3M(\frac{2R}{\pi})}{M + 3M} = \frac{\frac{4MR}{\pi}}{4M} = \frac{R}{\pi}$.

Two semicircular rings of linear mass densities $\lambda$ and $3 \lambda$ and of radius $R$ each,are joined to form a complete ring. The distance of the centre of mass of the complete ring from its geometrical centre is

Similar Questions

The electron affinity of sulfur is........

If the charge on the capacitor is increased by $2 \ C$,the energy stored in it increases by $21 \%$. The total original charge on the capacitor is: (in $C$)

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to

Which of the following is $NOT$ a characteristic of the phylum $Annelida$?

Which of the following oxides will not react with $NaOH$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module