Question

two metal spheres of mass 3 kg and 2kg are moving in the opposite direction with velocity of 15 metre per second and 10 metre per second respectively after the collision is they sticks to each other and a travel simultaneous please find the velocity after collision...​

Answer 1

$\large \clubs \:  \bf Given :  -$

• Two metal spheres of mass 3 kg and 2kg are moving in the opposite direction with velocity of 15 m/s and 10 m/s.

• After the collision is they sticks to each other and a travel combined.

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$\large \clubs \:  \bf To \: Find :  -$

• Velocity of Combination after Collision.

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$\large \clubs \:  \bf Solution :  -$

We Have,

Mass of First Sphere = m₁ = 3kg

Initial velocity of 1st Sphere =

u₁ = 15m/s

• Mass of Second Sphere = m₂ = 2kg

Initial velocity of 2nd Sphere =

u₂ = -10 m/s

( - ve Sign denotes that the velocity is in opposite direction )

As After Collision both sticks :

So,

Mass of Combination = M = 3 + 2

⇝ Mass of Combination = M = 5kg .

✏ By Conservation of Momentum :

$\red{ \text{Initial Momentum = Final Momentum }}$

$:\longmapsto \text m_1 \text u_1+ \text m_2 \text u_2= \text{MV}$

✏ Putting Given Values We Get :

$3 \times 15 + 2 \times ( - 10) = 5 \times \text V$

$:\longmapsto 5\text V = {45 - 20}$

$:\longmapsto5\text V = 25$

$:\longmapsto\text V = \cancel\dfrac{25}{5}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf  V = 5\:m/s} }}}$

$\underline{\pink{\underline{\frak{\pmb{ \text So, \text Velocit\text y \: after \: Collision = 5 \: m/s }}}}}$

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Answer 2

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

Two metal spheres of mass 3 kg and 2kg are moving in the opposite direction with velocity of 15 metre per second and 10 metre per second respectively after the collision is they sticks to each other and a travel simultaneous please find the velocity after collision

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

Given that :

• Mass (m₁) = 3 kg

• Mass (m₂) = 2 kg

• Initial Velocity (u₁) = 15 m/s

• Initial Velocity (u₂) = - 10 m/s

Now,

We know that Momentum formula is :

$\green{ \underline{ \boxed{ \blue{\sf Momentum = m_{1} u_{1} + m_{2} u_{2} = v(m_{1} + m_{2})}}}}$

By applying this formula we get :

Rewriting the formula for clear relationship of the values with the variables

• m₁u₁ + m₂u₂ = v(m₁ + m₂)

Putting the values we get

• 3 × 15 + 2 × (- 10) = v(3 + 2)

• 45 + (- 20) = v × 5

• 45 - 20 = 5v

By cross multiplying we get

• 25/5 = v

• v = 5 m/s

$\:\:\: \star \: \green{ \underline{ \purple{\boxed{ \blue{\sf Hence, \: the \: Final \: Velocity \: after \: collision \: is \: 5 \: m/s}}}}}$