Question

two balls of 500 gram throwing with velocity 20 metre per second and 25 metre per second after sometime they stick together calculate the common velocity of balls
please I request to you please give answer my exam is going on​

Answer 1

Answer :-

22.5m/s

Explanation :-

Given :

• Mass of the first ball,m_1 = 500g = 0.5kg [1g = 1/1000]

• Mass of the second ball,m_2 = 500g = 0.5kg [1g = 1/1000]

• Initial velocity of the first ball,u_1 = 20m/s

• Initial velocity of the second ball,u_2 = 25m/s

To Find :

• Common velocity of the two balls = ?

Solution :

As no external force is acting upon the system the total momentum of the system is conserved.

According to the law of conservation of momentum

$\sf{}m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Put their values and solve it,

$\sf{}:\implies 0.5kg\times 20m/s+0.5\times 25=0.5kg\times v+0.5kg\times v$

$\sf{}:\implies 0.5m/s\times 20m/s+0.5kg\times 25m/s=0.5m/s\times v+0.5m\s\times v$

$\sf{}:\implies 10.0kg\ m/s+ 12.5kg\ m/s=(0.5m/s+0.5m/s)\times v$

$\sf{}:\implies 10.0kg\ m/s+ 12.5kg\ m/s=(1.0)\times v$

$\sf{}:\implies 22.5kg\ m/s=1v$

$\sf{}\therefore v = 22.5 m/s$

Therefore,final velocity of the two balls is equal to 22.5m/s

Answer 2

$\huge\bf{\underline{\underline{\gray{GIVEN:-}}}}$

• Same mass of two balls having mass 500g .

• Velocity of first ball = 20 m/s

• Velocity of second ball = 25 m/s

$\huge\bf{\underline{\underline{\gray{TO\:FIND:-}}}}$

• The common velocity of the system after they stick together .

$\huge\bf{\underline{\underline{\gray{SOLUTION:-}}}}$

Let,

• $\bf{{\red{Mass\:of\:1st\:ball\:}}\:=\:m_1\:}$ = 500 g = 0.5 kg

• $\bf{{\red{Mass\:of\:2nd\:ball\:}}\:=\:m_2\:}$ = 500 g = 0.5 kg

• $\bf{{\red{Velocity\:of\:1st\:ball\:}}\:=\:u_1\:}$ = 20m/s

• $\bf{{\red{Velocity\:of\:2nd\:ball\:}}\:=\:u_2\:}$ = 25m/s

✞︎ According to the "Law of conservation of momentum",

$\blue\bigstar\:\bf{\red{\overbrace{\underbrace{\purple{m_1\:u_1\:+\:m_2\:u_2\:=\:m_1\:v_1\:+\:m_2\:v_2\:}}}}}$

Let,

• $\bf\pink{v_1\:=\:v_2\:=\:common\:velocity\:(v)\:}$

$\bf{:\implies\:m_1\:u_1\:+\:m_2\:u_2\:=\:m_1\:v\:+\:m_2\:v\:}$

$\rm{:\implies\:0.5\times{20}\:+\:0.5\times{25}\:=\:0.5\times{v}\:+\:0.5\times{v}\:}$

$\rm{:\implies\:10\:+\:12.5\:=\:2\times{0.5\:v}\:}$

$\rm{:\implies\:22.5\:=\:1.0\:v\:}$

$\bf\green{:\implies\:v\:=\:22.5\:m/s\:}$

$\huge\red\therefore$ The common velocity of the system after they stick together is "22.5 m/s" .