Question

A particle of mass M having velocity V moving towards north collides with similar particle

moving with same velocity towards east. The two particles stick together and move towards

north east with a velocity

a.√2 V

b. V/√2

c. V/2

d. 2V​

Answer 1

Answer

North East with a velocity

2v

Answer 2

Answer:

The two particles stick together and move towards the northeast with a velocity of V/√2 i.e.(b).

Explanation:

We will use the concept of conservation of linear momentum to solve this question which is given as,

Initial momentum = final momentum                       (1)

From the question we have,

$\mathrm{MV\hat{i}+MV\hat{j}=2MV'}$                                   (2)

Where,

M=mass of the bodies

$\mathrm{V\hat{i}}$=velocity of the body moving towards the east

$\mathrm{V\hat{j}}$=velocity of the body moving towards the west

V'=final velocities of the body after they stick together

Now by solving equation (1) we get;

$\mathrm{M\sqrt{V^2+V^2} =2MV'}$

$\mathrm{M\sqrt{2V^2} =2MV'}$

$\mathrm{MV\sqrt{2} =2MV'}$

$\mathrm{V'=\frac{V\sqrt{2} }{2} }$

$\mathrm{V'=\frac{V}{\sqrt{2} } }$                 (3)

Hence, among the given options the correct answer is (b) i.e. V/√2.

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