Question

Two particles of masses 2 kg and 3 kg are projected horizontally in opposite directions from the top of a tower of height 39.2 m with velocities 5 m/s and 10 m/s respectively. The horizontal range of the centre of mass of two particles is

• A. $8\sqrt{2}m$ in the direction of 2 kg
• B. $16\sqrt{2}m$ in the direction of 3 kg
• C. $\sqrt{8}m$ in the direction of 2 kg
• D. $\sqrt{8}m$ in the direciton of 3 kg

Answer 1

Answer: (B)

$16\sqrt{2}m$ in the direction of 3 kg

Range of center of mass $R=V_{cm}\times T=V_{cm}\times \sqrt{\frac{2h}{g}}$

$V_{cm}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}{V}_{cm}=\frac{2\times 5+3\times 10}{2+3}=8$

$R=8\times \sqrt{\frac{2\times 39.2}{9.8}}$

$R=16\sqrt{2}$ in the direction of $3kg$.