The figure shows a composite system of two un | vedclass

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

Question

(C) Let the linear mass density of the rods be $\lambda$.The mass of the horizontal rod (length $L$) is $m_1 = \lambda L$ and its centre of mass is at

Vedclass · Accepted Answer

$\left(\frac{L}{6}, \frac{2 L}{3}\right)$

Vedclass · Answer

(C) Let the linear mass density of the rods be $\lambda$.The mass of the horizontal rod (length $L$) is $m_1 = \lambda L$ and its centre of mass is at $(x_1, y_1) = (L/2, 0)$.The mass of the vertical rod (length $2L$) is $m_2 = \lambda(2L) = 2m$ (where $m = \lambda L$) and its centre of mass is at $(x_2, y_2) = (0, L)$.The $x$-coordinate of the centre of mass is $x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} = \frac{m(L/2) + 2m(0)}{m + 2m} = \frac{mL/2}{3m} = \frac{L}{6}$.The $y$-coordinate of the centre of mass is $y_{cm} = \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2} = \frac{m(0) + 2m(L)}{m + 2m} = \frac{2mL}{3m} = \frac{2L}{3}$.Thus,the coordinates of the centre of mass are $\left(\frac{L}{6}, \frac{2L}{3}\right)$.

The figure shows a composite system of two uniform rods of lengths as indicated. The coordinates of the centre of mass of the system of rods are ...........

Similar Questions

$A$ thin uniform circular disc has mass $9M$ and radius $R$. $A$ small circular part of radius $R/3$ is cut from the disc as shown in the figure. Calculate the moment of inertia of the remaining part about an axis passing through the center $O$ and perpendicular to the plane of the disc.

The $(x, y)$ coordinates (in $cm$) of the centre of mass of letter $E$ relative to the origin $O$,whose dimensions are shown in the figure are: (Take width of the letter $2 \ cm$ everywhere).

The coordinates of the centre of mass of a uniform $L$-shaped plate of mass $3 \ kg$ shown in the figure is:

$A$ circular disc of radius $R$ is cut from a thin metal plate. $A$ hole of radius $R/2$ is cut from this disc such that it touches the rim of the original disc. Find the distance of the center of mass of the remaining part from the center of the original disc.

From a circular disc of radius $R$,a triangular portion is cut as shown in the figure. The distance of the center of mass $(COM)$ of the remaining disc from the center of the disc $O$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module