Question

two bodies of 2kg and 4kg are moving with velocities 20m/s and 10m/s respectively towards each other under mutual gravitational attraction find the velocity of their centre of mass in m/s​

Answer 1

Answer:

$\huge\underline\green{\sf Answer:}$

$\red{\boxed{\sf Heat\: Energy (Q) = 21001.4KJ}}$

Given :-

• Mass ( M¹ ) = 2kg
• Mass ( M² ) = 4kg
• Velocity ( V¹ = 20m/s
• Velocity ( V² = 40m/s

To find :-

Velocity of centre of mass ( Vcom ) = ?

We know -

$\blue{\boxed{\sf Vcom = M¹ \: V¹ + M² \: V² / M¹ \: + \: M² }}$

$= \frac{2 \times 20 - 4 \times 40}{2 + 4}$

[ Negative (-) because both are moving in opposite direction ]

$= \frac{40 - 160}{6}$

$= - \frac{120}{6}$

$\purple{\boxed{\sf Vcom = -20m / s }}$

Answer 2

Answer:

Velocity of their centre of mass is zero m/s.

Explanation:

Given;-

       Mass, m₁ = 2 kg

                 m₂ = 4 kg

  Velocity, v₁ = 20 m/s

                 v₂ = 10 m/s

Now, since both the bodies are moving towards each other, we assume the direction of velocity of one of the bodies to be negative. Here, let v₂ be negative.

We know that, by formula;

            Vcm = v₁m₁ + v₂m₂ / m₁ + m₂

Note; Vcm represents velocity of centre of mass.

             Vcm = 20 × 2 - 10 × 4/  4 + 2

             Vcm = 40 - 40 / 6

             Vcm = 0/6

             Vcm = 0 m/s

Hope it helps! ;-))