First slide

Location of centre on mass for multiple point masses

Question

A circular ring of mass 6 kg and radius a is placed such that its centre lies at the origin. Two particles of masses 2 kg each are placed at the intersecting points of the circle with positive X-axis and positive Y-axis. Then, the angle made by the position vector of centre of mass of entire system with X-axis is

Moderate

A

45°
B

60°
C

$\tan^{- 1} (\frac{4}{5})$
D

30°

Solution

P is the position of centre of mass of particles at 2 and 3.
Q is position of centre of mass of all three particles.
$\tan θ = \frac{y_{CM}}{x_{CM}} = \frac{m_{1} y_{1} + m_{2} y_{2} + m_{3} y_{3}}{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}$
$= \frac{6 \times 0 + 2 \times 0 + 2 \times a}{6 \times 0 + 2 \times a + 2 \times 0} = 1$ or $θ = 45^{\circ}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App