Answer

Verified

35.4k+ views

**Hint:**For this we use the law of conservation of momentum which is momentum before and after collision is always conserved. And also use the equation of conservation of energy that energy is conserved before and after collision.

**Complete step by step solution:**

As we have a block of mass m move with initial velocity $\vec u$ and wedge with same mass m and initial velocity $\vec v$ .

Now according to the law of conservation of momentum: For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

Therefore, $mu = \left( {m + m} \right)v$

Because after collision both the objects are combined so add their mass and they move with the same mass that is $m$ .

$ \Rightarrow mu = 2mv$

After calculating for $v$

$\therefore v = \dfrac{u}{2}$

After that we have an energy equation According to this total energy means potential and kinetic energy is equal before and after collision.

$\dfrac{1}{2}m{u^2} = mgH + \dfrac{1}{2}m{v^2} + \dfrac{1}{2}m{v^2}$

Because in starting only kinetic energy of block is in act whose velocity is $u$ and after that potential energy as well as kinetic energy of block and wedge is in act with common velocity $v$ .

$\dfrac{1}{2}m{u^2} = mgh + \dfrac{1}{2}m{\left( {\dfrac{u}{2}} \right)^2} + \dfrac{1}{2}m{\left( {\dfrac{u}{2}} \right)^2}$ (Insert value of $v$)

$\dfrac{1}{2}m{u^2} = mgh + \dfrac{1}{4}m{u^2}$

Now, like terms should be on same side

$\dfrac{1}{2}m{u^2} - \dfrac{1}{4}m{u^2} = mgh$

After subtraction

$ \Rightarrow \dfrac{1}{4}m{u^2} = mgh$

By cancelling $m$ we have velocity which is equal to

${u^2} = 4gh$

$\therefore u = 2\sqrt {gh} $

**So, Option (A) is correct.**

**Note:**Always remember about kinetic energy and potential energy which one is come into action. Otherwise the answer will be wrong and also in momentum conservation law remember that $2\sqrt {gh} $ both objects combined and move with the same velocity.

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

f a body travels with constant acceleration which of class 1 physics JEE_Main

A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main

If the beams of electrons and protons move parallel class 1 physics JEE_Main

Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Other Pages

Oxidation state of S in H2S2O8 is A 6 B 7 C +8 D 0 class 12 chemistry JEE_Main

Two identical charged spheres suspended from a common class 12 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

Explain the construction and working of a GeigerMuller class 12 physics JEE_Main

In a CO molecule the distance between C mass12 amu class 12 physics JEE_Main

A gas is compressed isothermally to half its initial class 11 physics JEE_Main