Question

A billiard ball of mass 45 g moving
at a speed of 10 m s-strikes
another ball of mass 30 g at rest.
Now both the balls move together.
Find the common velocity.

Answer 1

Answer :-

Common velocity is 6 m/s .

Explanation :-

We have :-

→ Mass of 1st ball (m₁) = 45 g

→ Mass of 2nd ball (m₂) = 30 g

→ Velocity of 1st ball (u₁) = 10 m/s

→ Velocity of 2nd ball (u₂) = 0 m/s

To find :-

→ Common velocity of the balls .

________________________________

From the question, we have understood that the 1st ball strikes the 2nd ball (initially at rest) and then the two balls move together. So, let their common velocity be v m/s .

On applying "Law of Conservation of Momentum", we have :-

m₁u₁ + m₂u₂ = (m₁ + m₂)v

⇒ 45(10) + 30(0) = (45 + 30)v

⇒ 450 + 0 = 75v

⇒ 450 = 75v

⇒ v = 450/75

⇒ v = 6 m/s

Answer 2

Question :-

A billiard ball of mass 45 g moving at a speed of 10 m s-strikes another ball of mass 30 g at rest. Now both the balls move together. Find the common velocity.

Answer :-

• The common velocity is 6m/s

Step by step explanation :-

We have given that,

• The mass of 1st ball is 45g and velocity is 10m/s and the mass of 2nd ball is 30g at rest then we can assume the velocity be 0m/s.

All the data we can written as,

Let,

mass be m and velocity be u

$\rm{➨ \: m_{1} = 45g} \: \: \: \: \\ \rm{➨ \: u_{1} = 10m/s} \\ \rm{➨ \: m_{2} = 30g} \: \: \: \: \\ \rm{➨ \: u_{2} = 0m/s} \: \:$

Applying Law of conservation of momentum,

Law is :-

$\rm:\longmapsto{m_1 u _1 + m_2 u_2 = ( m_1 + m_2 ) v}</p><p>$

On substituting all values,

$\rm:\longmapsto{45(10) + 30(0) = (45 + 30)v} \\ \\ \rm:\longmapsto{450 = 75v} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{v = \frac{450}{75} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{v = 6m/s} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬