An ideal spring is connected between two blocks of masses $M$ and $m$. This system can move on a smooth horizontal table. The blocks are brought closer to compress the spring and then released. In the subsequent motion,select the true statement$(s)$:
$(a)$ They move in opposite directions with speeds inversely proportional to their masses.
$(b)$ The ratio of their speeds remains constant.
$(c)$ Linear momentum and energy of the system remain conserved.
$(a)$ They move in opposite directions with speeds inversely proportional to their masses.
$(b)$ The ratio of their speeds remains constant.
$(c)$ Linear momentum and energy of the system remain conserved.
- Aonly $a$
- Bboth $a$ and $c$
- Conly $c$
- D$a, b$ and $c$
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View SolutionColumn $II$ shows five systems in which two objects are labelled as $X$ and $Y$. Also in each case a point $P$ is shown. Column $I$ gives some statements about $X$ and/or $Y$. Match these statements to the appropriate system$(s)$ from Column $II$.
Column $I$ Column $II$ $(A)$ The force exerted by $X$ on $Y$ has a magnitude $Mg$. $(p)$ Block $Y$ of mass $M$ on a fixed inclined plane $X$,slides on it with a constant velocity. $(B)$ The gravitational potential energy of $X$ is continuously increasing. $(q)$ Two ring magnets $Y$ and $Z$,each of mass $M$,are kept in a frictionless vertical plastic stand. $Y$ rests on base $X$ and $Z$ hangs in equilibrium. The system is in a lift moving up with constant velocity. $(C)$ Mechanical energy of the system $X+Y$ is continuously decreasing. $(r)$ $A$ pulley $Y$ of mass $m_0$ is fixed to a table $X$. $A$ block of mass $M$ hangs from a string over the pulley,fixed at $P$. The system is in a lift moving down with constant velocity. $(D)$ The torque of the weight of $Y$ about point $P$ is zero. $(s)$ $A$ sphere $Y$ of mass $M$ is released in a non-viscous liquid $X$ and moves down. $(t)$ $A$ sphere $Y$ of mass $M$ is falling with terminal velocity in a viscous liquid $X$.
| Column $I$ | Column $II$ |
|---|---|
| $(A)$ The force exerted by $X$ on $Y$ has a magnitude $Mg$. | $(p)$ Block $Y$ of mass $M$ on a fixed inclined plane $X$,slides on it with a constant velocity. |
| $(B)$ The gravitational potential energy of $X$ is continuously increasing. | $(q)$ Two ring magnets $Y$ and $Z$,each of mass $M$,are kept in a frictionless vertical plastic stand. $Y$ rests on base $X$ and $Z$ hangs in equilibrium. The system is in a lift moving up with constant velocity. |
| $(C)$ Mechanical energy of the system $X+Y$ is continuously decreasing. | $(r)$ $A$ pulley $Y$ of mass $m_0$ is fixed to a table $X$. $A$ block of mass $M$ hangs from a string over the pulley,fixed at $P$. The system is in a lift moving down with constant velocity. |
| $(D)$ The torque of the weight of $Y$ about point $P$ is zero. | $(s)$ $A$ sphere $Y$ of mass $M$ is released in a non-viscous liquid $X$ and moves down. |
| $(t)$ $A$ sphere $Y$ of mass $M$ is falling with terminal velocity in a viscous liquid $X$. |
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