A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

221951-q

  • [JEE MAIN 2024]
  • A

    $\sqrt{6} \mathrm{~m}$

  • B

    $2 \mathrm{~m}$

  • C

    $1 \mathrm{~m}$

  • D

    $\sqrt{5} \mathrm{~m}$

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A body of mass $1\,kg$ falls freely from a height of $100\,m,$ on a platform of mass $3\,kg$ which is mounted on a spring having spring constant $k = 1.25 \times 10^6\, N/m.$ The body sticks to the platform and the spring’s maximum compression is found to be $x.$ Given that $g = 10\,ms^{-2},$ the value of $x$ will be close to ................ $\mathrm{cm}$

  • [JEE MAIN 2019]

Mention the work done by spring force in cylic process.

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:

$A$: standing on the horizontal surface

$B$: standing on the block 

To an observer $A$, the work done by spring force is 

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:

$A$: standing on the horizontal surface

$B$: standing on the block 

According to observer $B$, the potential energy of the spring increases

A spring of force constant $k$ is cut in two parts at its one third length. When both the parts are stretched by same amount, the work done in the two parts, will be