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Three masses are placed on the x-axis : ...

Three masses are placed on the x-axis : `300 g` at origin. `500 g` at `x = 40 cm` and `400 g` at `x = 70 cm`. The distance of the centre of mass from the origin is.

A

45 cm

B

50 cm

C

30 cm

D

40 cm

Text Solution

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The correct Answer is:
To find the center of mass of the three masses placed on the x-axis, we can use the formula for the center of mass (CM): \[ \text{CM} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3} \] ### Step-by-Step Solution: 1. **Identify the masses and their positions:** - Mass \( m_1 = 300 \, \text{g} \) at position \( x_1 = 0 \, \text{cm} \) - Mass \( m_2 = 500 \, \text{g} \) at position \( x_2 = 40 \, \text{cm} \) - Mass \( m_3 = 400 \, \text{g} \) at position \( x_3 = 70 \, \text{cm} \) 2. **Substitute the values into the center of mass formula:** \[ \text{CM} = \frac{(300 \times 0) + (500 \times 40) + (400 \times 70)}{300 + 500 + 400} \] 3. **Calculate the numerator:** - Calculate each term: - \( 300 \times 0 = 0 \) - \( 500 \times 40 = 20000 \) - \( 400 \times 70 = 28000 \) - Add these values together: \[ 0 + 20000 + 28000 = 48000 \] 4. **Calculate the denominator:** \[ 300 + 500 + 400 = 1200 \] 5. **Calculate the center of mass:** \[ \text{CM} = \frac{48000}{1200} = 40 \, \text{cm} \] ### Final Answer: The distance of the center of mass from the origin is \( 40 \, \text{cm} \). ---
To find the center of mass of the three masses placed on the x-axis, we can use the formula for the center of mass (CM): \[ \text{CM} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3} \] ### Step-by-Step Solution: ...
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