An object of mass $m$ is performing simple harmonic motion on a smooth horizontal surface as shown in the figure. Just as the oscillating object reaches its extreme position, another object of mass $2 \mathrm{m}$ is dropped on to oscillating object, which sticks to it. For this situation mark out the correct statement(s).

The given Fig. (a) shows a spring of force constant $k$ fixed at one end and carrying a mass $m$ at the other end placed on a horizontal frictionless surface. The spring is stretched by a force $F.$ Figure (b) shows the same spring with both ends free and a mass $m$ fixed at each free end. Each of the spring is stretched by the same force $F.$ The mass in case (a) and the masses in case (b) are then released. Which of the following statements are true?

Two blocks connected by a spring rest on a smooth horizontal plane as shown in the given figure. A constant force $F$ starts acting on block $m_2$ as shown in the figure. Which of the following statements are not correct?

A cylindrical block of density $d$ stays fully immersed in a beaker filled with two immiscible liquids of different densities $d_1$ and $d_2.$ The block is in equilibrium with half of it in liquid $1$ and the other half in liquid $2$ as shown in the given figure. If the block is given a displacement downwards and released, then neglecting friction study the following statements.

As shown in the figure a horizontal platform with a mass $m$ placed on it is executing SHM along $y$-axis. If the amplitude of oscillation is $2.5 \mathrm{cm}$, the minimum period of the motion for the mass not to be detached from the platform is: $(g= 10 \mathrm{m} {\sec }^{-2} = {\mathrm{\pi }}^2)$