Four masses 1 kg, 1 kg, 2 kg and 2 kg are | vedclass

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

Question

(D) Let the square be in the $XY$-plane with $P(0, a), Q(a, a), R(a, 0)$ and $S(0, 0)$.The masses are $m_P = 1 \ kg, m_Q = 1 \ kg, m_R = 2 \ kg, m_S =

Vedclass · Accepted Answer

$P$ and $Q$

Vedclass · Answer

(D) Let the square be in the $XY$-plane with $P(0, a), Q(a, a), R(a, 0)$ and $S(0, 0)$.The masses are $m_P = 1 \ kg, m_Q = 1 \ kg, m_R = 2 \ kg, m_S = 2 \ kg$.The center of mass of $P$ and $S$ is at $O_1$ on the side $PS$ at a distance $y_1 = \frac{m_P \cdot a + m_S \cdot 0}{m_P + m_S} = \frac{1 \cdot a + 2 \cdot 0}{1 + 2} = \frac{a}{3}$ from $S$.The center of mass of $Q$ and $R$ is at $O_2$ on the side $QR$ at a distance $y_2 = \frac{m_Q \cdot a + m_R \cdot 0}{m_Q + m_R} = \frac{1 \cdot a + 2 \cdot 0}{1 + 2} = \frac{a}{3}$ from $R$.The total mass of the system is $M = 1 + 1 + 2 + 2 = 6 \ kg$.The center of mass of the whole system lies on the line joining $O_1$ and $O_2$ at a distance $x_{cm} = \frac{(m_P+m_S) \cdot 0 + (m_Q+m_R) \cdot a}{M} = \frac{3 \cdot 0 + 3 \cdot a}{6} = \frac{a}{2}$ from the $Y$-axis.Thus,the center of mass is at $(\frac{a}{2}, \frac{a}{3})$.Comparing distances from corners: The center of mass is closest to $R$ and $S$ (distance $\sqrt{(a/2)^2 + (a/3)^2}$) and farthest from $P$ and $Q$ (distance $\sqrt{(a/2)^2 + (2a/3)^2}$).

Four masses $1 \ kg, 1 \ kg, 2 \ kg$ and $2 \ kg$ are placed at the four corners $P, Q, R$ and $S$ of a square of side $a$ respectively. The center of mass of the system will be farthest from which of the following?

Similar Questions

Particles of masses $m, 2m, 3m, \ldots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \ldots, nl$ cm from a fixed point. The distance of the centre of mass of the particles from the fixed point in centimetres is:

Two bodies of mass $1\,kg$ and $3\,kg$ have position vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The magnitude of the position vector of the centre of mass of this system will be equal to the magnitude of which of the following vectors?

An object comprises a uniform ring of radius $R$ and its uniform chord $AB$ (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of the object?

What is the position of the centre of mass of symmetrical and homogeneous bodies?

On what does the position of the center of mass of a rigid body depend?

Vedclass Test Series

Exam Paper Generator

Online Exam Module