$STATEMENT$-$1$ A block of mass $\mathrm{m}$ starts moving on a rough horizontal surface with a velocity $\mathrm{v}$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. because
$STATEMENT$- $2$ The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.
$STATEMENT$-$1$ A block of mass $\mathrm{m}$ starts moving on a rough horizontal surface with a velocity $\mathrm{v}$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. because
$STATEMENT$- $2$ The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.
- [IIT 2007]
- A
Statement -$1$ is True, Statement-$2$ is True; Statement-$2$ is a correct explanation for statement-$1$.
- B
Statement -$1$ is True, Statement-$2$ is True; Statement-$2$ is $NOT$ a correct explanation for statement-$1$.
- C
Statement -$1$ is True, Statement-$2$ is False.
- D
Statement -$1$ is False, Statement- $2$ is True.
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- [IIT 2009]
A bullet of mass $20 \,g$ leaves a riffle at an initial speed $100 \,m / s$ and strikes a target at the same level with speed $50 \,m / s$. The amount of work done by the resistance of air will be ......... $J$
A bullet of mass $20 \,g$ leaves a riffle at an initial speed $100 \,m / s$ and strikes a target at the same level with speed $50 \,m / s$. The amount of work done by the resistance of air will be ......... $J$
Column $II$ shows five systems in which two objects are labelled as $\mathrm{X}$ and $\mathrm{Y}$. Also in each case a point $\mathrm{P}$ is shown. Column $I$ gives some statements about $\mathrm{X}$ and/or $\mathrm{Y}$. Match these statements to the appropriate system$(s)$ from Column $II$.
Column $I$
Column $II$
$(A)$ The force exerted by $\mathrm{X}$ on $\mathrm{Y}$ has a magnitude $\mathrm{Mg}$.
$Image$ Block $Y$ of mass $M$ left on a fixed inclined plane $\mathrm{X}$, slides on it with a constant velocity.
$(B)$ The gravitational potential energy of $\mathrm{X}$ is continuously increasing.
$Image$ Two ring magnets $\mathrm{Y}$ and $\mathrm{Z}$, each of mass $M$, are kept in frictionless vertical plastic stand so that they repel each other. $Y$ rests on the base $X$ and $\mathrm{Z}$ hangs in air in equilibrium. $\mathrm{P}$ is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity.
$(C)$ Mechanical energy of the system $\mathrm{X}+\mathrm{Y}$ is continuously decreasing.
$Image$ A pulley $Y$ of mass $m_0$ is fixed to a table through a clamp $X$. A block of mass $M$ hangs from a string that goes over the pulley and is fixed at point $\mathrm{P}$ of the table. The whole system is kept in a lift that is going down with a constant velocity.
$(D)$ The torque of the weight of $\mathrm{Y}$ about point $\mathrm{P}$ is zero.
$Image$ A sphere $\mathrm{Y}$ of mass $M$ is put in a nonviscous liquid $\mathrm{X}$ kept in a container at rest. The sphere is released and it moves down in the liquid.
$Image$ A sphere $\mathrm{Y}$ of mass $M$ is falling with its terminal velocity in a viscous liquid $\mathrm{X}$ kept in a container.
Column $II$ shows five systems in which two objects are labelled as $\mathrm{X}$ and $\mathrm{Y}$. Also in each case a point $\mathrm{P}$ is shown. Column $I$ gives some statements about $\mathrm{X}$ and/or $\mathrm{Y}$. Match these statements to the appropriate system$(s)$ from Column $II$.
| Column $I$ | Column $II$ |
| $(A)$ The force exerted by $\mathrm{X}$ on $\mathrm{Y}$ has a magnitude $\mathrm{Mg}$. | $Image$ Block $Y$ of mass $M$ left on a fixed inclined plane $\mathrm{X}$, slides on it with a constant velocity. |
| $(B)$ The gravitational potential energy of $\mathrm{X}$ is continuously increasing. | $Image$ Two ring magnets $\mathrm{Y}$ and $\mathrm{Z}$, each of mass $M$, are kept in frictionless vertical plastic stand so that they repel each other. $Y$ rests on the base $X$ and $\mathrm{Z}$ hangs in air in equilibrium. $\mathrm{P}$ is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity. |
| $(C)$ Mechanical energy of the system $\mathrm{X}+\mathrm{Y}$ is continuously decreasing. | $Image$ A pulley $Y$ of mass $m_0$ is fixed to a table through a clamp $X$. A block of mass $M$ hangs from a string that goes over the pulley and is fixed at point $\mathrm{P}$ of the table. The whole system is kept in a lift that is going down with a constant velocity. |
| $(D)$ The torque of the weight of $\mathrm{Y}$ about point $\mathrm{P}$ is zero. | $Image$ A sphere $\mathrm{Y}$ of mass $M$ is put in a nonviscous liquid $\mathrm{X}$ kept in a container at rest. The sphere is released and it moves down in the liquid. |
| $Image$ A sphere $\mathrm{Y}$ of mass $M$ is falling with its terminal velocity in a viscous liquid $\mathrm{X}$ kept in a container. |
- [IIT 2009]