In the figure, the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage, the minimum mass of $A$ must be
In the figure, the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage, the minimum mass of $A$ must be
- A
$2M$
- B
$M$
- C
$M/2$
- D
A function of $M$ and the force constant of the spring
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A particle is placed at the point $\mathrm{A}$ of a frictionless track $A B C$ as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point $B$ is: $\left(\right.$ Take $g=10 \mathrm{~m} / \mathrm{s}^2$ ).
A particle is placed at the point $\mathrm{A}$ of a frictionless track $A B C$ as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point $B$ is: $\left(\right.$ Take $g=10 \mathrm{~m} / \mathrm{s}^2$ ).
- [JEE MAIN 2024]
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to
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- [AIEEE 2004]
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]
$A$ small bucket of mass $M\, kg$ is attached to $a$ long inextensible cord of length $L\, m$ . The bucket is released from rest when the cord is in a horizontal position. At its lowest position, the bucket scoops up $m\, kg$ of water and swings up to a height $h$. The height $h$ in meters is
$A$ small bucket of mass $M\, kg$ is attached to $a$ long inextensible cord of length $L\, m$ . The bucket is released from rest when the cord is in a horizontal position. At its lowest position, the bucket scoops up $m\, kg$ of water and swings up to a height $h$. The height $h$ in meters is