Question

Two particles of masses 5 g and 3 g are separated by a distance of 40 cm. The centre of mass of the system of these two particles lies:

• A. lies at a distance of 15 cm from 5 g particle
• B. lies at a distance of 25 cm from 5 g particle
• C. lies at a distance of 10 cm from 3 g particle
• D. lies at the mid point of the line joining the two particles

Hint:

To calculate the center of mass for two objects, use the weighted average formula \( x_{\text{cm}} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \), where \( x_1 \) and \( x_2 \) are the positions of the masses.

Answer 1

The Correct Option is A

The center of mass \( x_{\text{cm}} \) for two masses is given by the formula: \[ x_{\text{cm}} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \] where: - \( m_1 = 5 \, \text{g} \), \( x_1 = 0 \) (position of 5 g mass at the origin), - \( m_2 = 3 \, \text{g} \), \( x_2 = 40 \, \text{cm} \) (position of 3 g mass 40 cm away). Substitute the values into the formula: \[ x_{\text{cm}} = \frac{(5 \times 0) + (3 \times 40)}{5 + 3} = \frac{120}{8} = 15 \, \text{cm} \] Thus, the center of mass lies 15 cm from the 5 g particle, and the correct answer is option (1).

Answer 2

Step 1: Write down the given data
Mass of first particle, \( m_1 = 5 \, \text{g} \)
Mass of second particle, \( m_2 = 3 \, \text{g} \)
Distance between particles, \( d = 40 \, \text{cm} \)

Step 2: Use the formula for centre of mass from \( m_1 \)
\[ x = \frac{m_2 \times d}{m_1 + m_2} \]
where \( x \) is the distance of the centre of mass from the \( m_1 \) particle.

Step 3: Calculate the distance \( x \)
\[ x = \frac{3 \times 40}{5 + 3} = \frac{120}{8} = 15 \, \text{cm} \]

Final answer: The centre of mass lies at a distance of 15 cm from the 5 g particle.