(A) Analysis of Column $I$ statements:$(A)$ Force by $X$ on $Y$ is $Mg$: In $(p)$,$N = Mg \cos \theta \neq Mg$. In $(q)$,$X$ supports $Y$,$N = Mg$. In

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$(A) \rightarrow p, t; (B) \rightarrow q; (C) \rightarrow s, t; (D) \rightarrow p, r, s, t$

(A) Analysis of Column $I$ statements:$(A)$ Force by $X$ on $Y$ is $Mg$: In $(p)$,$N = Mg \cos \theta \neq Mg$. In $(q)$,$X$ supports $Y$,$N = Mg$. In $(t)$,$X$ exerts buoyant force $F_B $(B)$ $GPE$ of $X$ increasing: $X$ is the frame/base. In $(q)$,the lift moves up,so $X$ moves up,$GPE$ increases.$(C)$ Mechanical energy decreasing: Occurs when non-conservative forces (friction/viscosity) do negative work. This happens in $(s)$ (if there were drag) or $(t)$ (viscous drag) and $(p)$ (friction).$(D)$ Torque of weight of $Y$ about $P$ is zero: If the line of action of weight passes through $P$. In $(p)$,$(r)$,$(s)$,and $(t)$,the geometry allows this.

Class 11 Physics Newton's Laws of Motion and Friction Mix Examples-Newton's Laws of Motion and Friction

Column $II$ 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 $X$.

IIT 2009 All IIT

A
$(A) \rightarrow p, t; (B) \rightarrow q; (C) \rightarrow s, t; (D) \rightarrow p, r, s, t$
B
$(A) \rightarrow p, t; (B) \rightarrow q; (C) \rightarrow s, t; (D) \rightarrow p, r, s, t$
C
$(A) \rightarrow p, t; (B) \rightarrow q; (C) \rightarrow s, t; (D) \rightarrow p, r, s, t$
D
$(A) \rightarrow p, t; (B) \rightarrow q; (C) \rightarrow s, t; (D) \rightarrow p, r, s, t$