$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It slides a distance $d$ along the track in time $t$ to reach position $2$, dropping a vertical distance $h$. Let $v$ and $a$ be the instantaneous speed and instantaneous acceleration, respectively, of the box at position $2$. Which of the following equations is valid for this situation?
$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It slides a distance $d$ along the track in time $t$ to reach position $2$, dropping a vertical distance $h$. Let $v$ and $a$ be the instantaneous speed and instantaneous acceleration, respectively, of the box at position $2$. Which of the following equations is valid for this situation?
- A
$h = vt$
- B
$h = (1/2)gt^2$
- C
$d = (1/2)at^2$
- D
$mgh = (1/2)mv^2$
Similar Questions
A number of identical cubical blocks of edge $'a'$ and mass $m$ are lying on a horizontal table. The work done on the blocks in arranging them in a column of height $(n + 1)a$ on the table is
A number of identical cubical blocks of edge $'a'$ and mass $m$ are lying on a horizontal table. The work done on the blocks in arranging them in a column of height $(n + 1)a$ on the table is
Column $II$ gives certain systems undergoing a process. Column $I$ suggests changes in some of the parameters related to the system. Match the statements in Column $I$ to the appropriate process$(es)$ from Column $II$.
Column $I$
Column $II$
$(A)$ The energy of the system is increased
$(p)$ $System:$ A capacitor, initially uncharged
$Process:$ It is connected to a battery
$(B)$ Mechanical energy is provided to the system, which is converted into energy of random motion of its parts
$(q)$ $System:$ A gas in an adiabatic container fitted with an adiabatic piston
$Process:$ The gas is compressed by pushing the piston
$(C)$ Internal energy of the system is converted into its mechanical energy
$(r)$ $System:$ A gas in a rigid container
$Process:$ The gas gets cooled due to colder atmosphere surrounding it
$(D)$ Mass of the system is decreased
$(s)$ $System:$ A heavy nucleus, initially at rest
$Process:$ The nucleus fissions into two fragments of nearly equal masses and some neutrons are emitted
$(t)$ $System:$ A resistive wire loop
$Process:$ The loop is placed in a time varying magnetic field perpendicular to its plane
Column $II$ gives certain systems undergoing a process. Column $I$ suggests changes in some of the parameters related to the system. Match the statements in Column $I$ to the appropriate process$(es)$ from Column $II$.
| Column $I$ | Column $II$ |
| $(A)$ The energy of the system is increased |
$(p)$ $System:$ A capacitor, initially uncharged $Process:$ It is connected to a battery |
| $(B)$ Mechanical energy is provided to the system, which is converted into energy of random motion of its parts |
$(q)$ $System:$ A gas in an adiabatic container fitted with an adiabatic piston $Process:$ The gas is compressed by pushing the piston |
| $(C)$ Internal energy of the system is converted into its mechanical energy |
$(r)$ $System:$ A gas in a rigid container $Process:$ The gas gets cooled due to colder atmosphere surrounding it |
| $(D)$ Mass of the system is decreased |
$(s)$ $System:$ A heavy nucleus, initially at rest $Process:$ The nucleus fissions into two fragments of nearly equal masses and some neutrons are emitted |
|
$(t)$ $System:$ A resistive wire loop $Process:$ The loop is placed in a time varying magnetic field perpendicular to its plane |
- [IIT 2009]
Under the action of a force, a $2 \,kg$ body moves such that its position $x$ as a function of time $t$ is given by $x=\frac{t^2}{3}$, where $x$ is in metres and $t$ in seconds. The workdone by the force in first two seconds is .......... $J$
Under the action of a force, a $2 \,kg$ body moves such that its position $x$ as a function of time $t$ is given by $x=\frac{t^2}{3}$, where $x$ is in metres and $t$ in seconds. The workdone by the force in first two seconds is .......... $J$
Figure here shows the frictional force versus displacement for a particle in motion. The loss of kinetic energy in travelling over $s = 0$ to $20\, m$ will be......$J$
Figure here shows the frictional force versus displacement for a particle in motion. The loss of kinetic energy in travelling over $s = 0$ to $20\, m$ will be......$J$
A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ................ $\mathrm{J}$
A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ................ $\mathrm{J}$
- [AIEEE 2004]