Question

a car of mass 1200 kg travelling with speed 60m/s on a straight road is ahead of a scooter having mass 80kg travelling with speed of 60m/s then what will be the speed of centre of mass of these vehicles??​​

Answer 1

Answer :

Mass of car = 1200kg

Velocity of bus = 60m/s

Mass of scooter = 80kg

Velocity of scooter = 60m/s

We have to find velocity of centre of mass.

For a system of N particles, the position of centre of mass is

$\displaystyle\dag\:\boxed{\bf{x_{CM}=\dfrac{\sum\limits_{i=1}^{N}\:m_i\:r_i}{\sum\limits_{i=1}^{N}\:m_i}}}$

On differentiating both sides wrt time,

$\displaystyle\dag\:\boxed{\bf{v_{CM}=\dfrac{\sum\limits_{i=1}^{N}\:m_i\:v_i}{\sum\limits_{i=1}^{N}\:m_i}}}$

★ Velocity of CM of a two particles system is

$\dag\:\boxed{\bf{v_{CM}=\dfrac{m_1v_1+m_2v_2}{m_1+m_2}}}$

By substituting the values, we get

$\implies\tt\:v_{CM}=\dfrac{(1200)(60)+(80)(60)}{1200+80}$

$\implies\tt\:v_{CM}=\dfrac{72000+4800}{1280}$

$\implies\tt\:v_{CM}=\dfrac{76800}{1280}$

$\implies\tt\:v_{CM}=60\:ms^{-1}$