Question

The system shown in the figure can move on a smooth surface. The spring is initially compressed by $6cm$ and then released:

• A. The particles perform SHM with time period $\frac{\pi }{10}sec$.
• B. The block of mass 3 kg perform SHM with amplitude $4cm$.
• C. The block of mass 6 kg will have maximum momentum 2.40 kgm / s
• D. Their time periods will be in the ratio of $1:\sqrt{2}$

Answer 1

Answer: (A), (B), (C)

As no external force is acting on the system both blocks will oscillate about their center of mass. If compression is $6cm$ then by mass moment property of center of mass we use $m_1\Delta x_1=m_2\Delta x_2$ so the amplitude of $3kg$ mass is $4cm$ and that of $6kg$ mass is $2cm$ hence option (B) is correct. The time period can be obtained either by using concept of reduced mass or by splitting the spring in two parts about center of mass of the two blocks in series combination which gives the $3kg$ block oscillates with a spring constant $1200N/m$ for which time period is $T=2\pi (m/k{)}^{1/2}=\pi /10$ sec hence option (A) is correct. The maximum momentum of $6kg$ block will be when it will pass through mean position and given as $mA\omega =2.4kgm/s$