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NEET PHYSICSEasy

Two particles of mass 5 kg5 \text{ kg} and 10 kg10 \text{ kg} respectively are attached to the two ends of a rigid rod of length 1 m1 \text{ m} with negligible mass. The centre of mass of the system from the 5 kg5 \text{ kg} particle is nearly at a distance of:

A

50 cm50 \text{ cm}

B

67 cm67 \text{ cm}

C

80 cm80 \text{ cm}

D

33 cm33 \text{ cm}

Step-by-Step Solution

Let the particle of mass m1=5 kgm_1 = 5 \text{ kg} be placed at the origin, so its position coordinate is x1=0x_1 = 0. The particle of mass m2=10 kgm_2 = 10 \text{ kg} is at a distance of 1 m=100 cm1 \text{ m} = 100 \text{ cm}, so its position coordinate is x2=100 cmx_2 = 100 \text{ cm}. The position of the centre of mass from the 5 kg5 \text{ kg} particle is given by: Xcm=m1x1+m2x2m1+m2X_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} Xcm=5(0)+10(100)5+10X_{cm} = \frac{5(0) + 10(100)}{5 + 10} Xcm=100015=2003 cm66.67 cmX_{cm} = \frac{1000}{15} = \frac{200}{3} \text{ cm} \approx 66.67 \text{ cm} Therefore, the centre of mass of the system from the 5 kg5 \text{ kg} particle is nearly at a distance of 67 cm67 \text{ cm}.

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