Answer

Verified

52.2k+ views

**Hint:**Recall that law of conservation of momentum that suggests that the initial and final momenta of a system are equal, which means that the momentum of a system remains constant throughout time. Now, since the particle is initially at rest the initial momentum will be zero.

Now, calculate an expression for the final momentum of the system by summing the individual particle momenta and equate it to the zero initial momentum and get the relation between the velocities of the two particles. This will give you the required answer.

**Formula used:**

Law of conservation of momentum: $p_{i} = p_{f}$, where $p_i$ is the initial momentum of a system and $p_f$ is the final momentum of the system.

**Complete answer:**

To work on this question, we make use of the Law of Conservation of Momentum.

According to this law, the total momentum of an isolated system remains constant, which means that the momentum of the system is conserved at any time. This suggests that there is no creation or destruction of momentum and in any case, there is only a transfer of momentum within the constituents of this system.

Thus, this law tells us that the initial and final momenta of the system are equal.

Now let us look at the situation given to us.

We first have a particle of say, mass m that is at rest.

Therefore, the initial momentum of the system $\vec{p_i} = m(0) = 0\;kgms^{-1}$

Now, this particle disintegrates into two particles of equal masses that start moving. This means that $m_1 = m_2 = \dfrac{m}{2}$, and let them move with a velocity $\vec{v_1}$ and $\vec{v_2}$ respectively.

Therefore, the final momentum of this system $\vec{p_f} = \dfrac{m}{2}\vec{v_1} + \dfrac{m}{2}\vec{v_2}$

From the law of conservation of momentum, we have:

$\vec{p_i} = \vec{p_f}$

$\Rightarrow 0 = \dfrac{m}{2}\vec{v_1} + \dfrac{m}{2}\vec{v_2} \Rightarrow 0 = \dfrac{m}{2}(\vec{v_1} +\vec{v_2})$

$\Rightarrow 0 = \vec{v_1} + \vec{v_2} \Rightarrow \vec{v_1} = -\vec{v_2}$

This means that both the particles move with the same speed after disintegration but move in opposite directions, as is indicative from the negative sign of the velocity vector.

**Thus, the correct option would be D. Move opposite with equal speed.**

**Note:**While using vector forms of quantities it becomes highly important to ensure that the signs associated with each vector are verified and accounted for, since represented a quantity as a vector implies that we are taking into consideration the directional information that it provides in addition to its magnitude, and any inconsistency in the signs will result in a wrongly oriented vector, which is not the result we want to get.

Recently Updated Pages

In a family each daughter has the same number of brothers class 10 maths JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

If 81 is the discriminant of 2x2 + 5x k 0 then the class 10 maths JEE_Main

What is the value of cos 2Aleft 3 4cos 2A right2 + class 10 maths JEE_Main

If left dfracleft 2sinalpha rightleft 1 + cosalpha class 10 maths JEE_Main

The circumference of the base of a 24 m high conical class 10 maths JEE_Main

Other Pages

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

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

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Which of the following sets of displacements might class 11 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main

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