A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36 \mathrm{~kg}$ and $0.72 \mathrm{~kg}$. Taking $g=10 \mathrm{~m} / \mathrm{s}^2$, find the work done (in joules) by the string on the block of mass $0.36 \mathrm{~kg}$ during the first second after the system is released from rest.
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36 \mathrm{~kg}$ and $0.72 \mathrm{~kg}$. Taking $g=10 \mathrm{~m} / \mathrm{s}^2$, find the work done (in joules) by the string on the block of mass $0.36 \mathrm{~kg}$ during the first second after the system is released from rest.
- [IIT 2009]
- A
$5$
- B
$6$
- C
$8$
- D
$9$
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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]
The graph between the resistive force $ F$ acting on a body and the distance covered by the body is shown in the figure. The mass of the body is $25\, kg$ and initial velocity is $2\, m/s$. When the distance covered by the body is $4m$, its kinetic energy would be .............. $\mathrm{J}$
The graph between the resistive force $ F$ acting on a body and the distance covered by the body is shown in the figure. The mass of the body is $25\, kg$ and initial velocity is $2\, m/s$. When the distance covered by the body is $4m$, its kinetic energy would be .............. $\mathrm{J}$