Question

A 2 kg body and 3 kg body are moving along x - axis with velocities 3 ms–1 respectively. The momentum CM is [ ] a) 6 kg ms–1 b) 9 kg ms–1 c) 3 kg ms–2 d) –3kg ms–1

Answer 1

Given :

Mass of first body = 2 kg

Mass of second body = 3 kg

Velocities along x axis :

$= 3 \frac{m}{s}$

To find :

Momentum of center of mass

Solution :

Momentum of an object is equal to mass times velocity of that object. The change in momentum with respect to time is called force .

Mass of first body :

$m_1 = 2 kg$

Mass of second body :

$m_2 = 3 kg \:$

Velocities of both bodies along x axis :

$= 3 \hat i \: \frac{m}{s}$

So,

Formula of momentum :

$\bf \: p = m \times v$

where,

p = momentum of body,

m = mass of body,

v = velocity of body.

So,

Momentum of first body :

$\bf \: p_1 = 2 \times 3 \hat i = 6 \hat i$

Momentum of second body :

$\bf \: p_2 = 3 \times 3 \hat i = 9 \hat i$

The formula of momentum with respect to center of mass :

$\bf \: p = \frac{(m_1 \times p_1) + (m_2 \times p_2)}{m_1 + m_2}$

Putting values of all the masses of bodies and their respective momentum ,

The momentum of center of mass :

$\bf \: p = \frac{(2 \times 6\hat i) + (3 \times 9\hat i)}{2 + 3}$

$\bf \: p = \frac{(12\hat i) + (27\hat i )}{5}$

$\bf \: p = \frac{39\hat i}{5} = 7.8 \hat i \:$

So,

The momentum of center of mass:

p = 7.8 meter per second.

Note :

In this question,

the same velocity is given for both the bodies which is either miss print,

It is a basic way to solve these kind of problems.