# What is the momentum of the block before collision if the block having mass M is moving on the frictionless horizontal surface collides with a spring of constant K and compresses by L?

(A) $L\sqrt {MK} $

(B) $\dfrac{{K{L^2}}}{{2M}}$

(C) Zero

(D) $\dfrac{{M{L^2}}}{K}$

Answer

Verified

289.2k+ views

**Hint**Use the formula,

$K.E + P.E = E$

where, $K.E$ is the kinetic energy

$P.E$ is the potential energy

$E$ is the energy

Then, make use of the conservation of energy by making kinetic energy and potential energy equal to each other.

**Step by Step Solution**

We know that, if conservative forces acts on system only the mechanical energy remains constant

$\therefore K.E + P.E = E$(constant)

where, $K.E$ is the kinetic energy

$P.E$ is the potential energy

$E$ is the mechanical energy which is constant

$

\Delta K + \Delta U = 0 \\

\\

$

Therefore, $\Delta K = - \Delta U$

Let the initial velocity be $v$

then, kinetic energy is $\dfrac{1}{2}m{v^2}$

And final potential energy due to spring is $\dfrac{1}{2}k{x^2}$ (where, $x$is the compression)

According to conservation of energy, the energy inside a closed system remains constant

So, the kinetic energy becomes equal to the final potential energy

Therefore, $\dfrac{1}{2}M{v^2} = \dfrac{1}{2}K{x^2}$

$

M{v^2} = K{x^2} \\

{v^2} = \dfrac{{K{x^2}}}{M} \\

v = x\sqrt {\dfrac{K}{M}} \\

$

Here, $x$is the compression. So, according to question $L = $compression

$\therefore v = L\sqrt {\dfrac{K}{M}} \cdots (1)$

Hence, maximum momentum, $P = Mv$

Using the value of $v$ from equation $(1)$ in the formula of momentum

$P = L\sqrt {MK} $

**From above, we can say that option (A) is correct.**

**Note**The mechanical energy remains constant when conservative forces act only on the system.

In the conservation of energy, we can say that the two energies become equal to each other because energy inside the closed system remains constant therefore, both become equal.

Momentum is the product of mass and velocity and is denoted by $P$ so, we can express momentum as:

$P = Mv$

Last updated date: 31st May 2023

•

Total views: 289.2k

•

Views today: 6.46k

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

A ball impinges directly on a similar ball at rest class 11 physics CBSE

Lysosomes are known as suicidal bags of cell why class 11 biology CBSE

How do you define least count for Vernier Calipers class 12 physics CBSE

Two balls are dropped from different heights at different class 11 physics CBSE

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main