Question

Two particles of masses $2kg$ and $3kg$ are projected horizontally in opposite directions from the top of a tower of height $39.2m$ with velocities $5ms^{- 1}$ and $10ms^{- 1}$ respectively. The horizontal range of the centre of mass of two particles is [ $g=9.8ms^{- 2}$ ]

• A. $8\sqrt{2}$ m in the direction of 2 kg
• B. $8\sqrt{2}$ m in the direction of 3 kg
• C. $\sqrt{8}$ m in the direction of 2 kg
• D. $\sqrt{8}$ m in the direction of 3 kg

Answer 1

Answer: (B)

Range of C.M $=V_{c m}\sqrt{\frac{2 h}{g}}$
$V_{c m}=\frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}}$
$V_{c o m} = \frac{- 2 \times 5 + 3 \times 10}{2 + 3} = 4 m / s$
Range $= 4 \sqrt{\frac{2 \times 39.2}{9.8}} = 8 \sqrt{2}$