Question

a bomb of mass 9 kg explodes into two pieces of masses 3kg and 6 kg the velocity of mass 3 kg is 16 metre per second calculate the kinetic energy of mass 6 kg ​

Answer 1

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Explanation:

GIVEN:

M1=3kg

M2 = 6kg

V1 = 16m/s

TO FIND:

K.E 2 = ?

According to law of conservation of momentum :

(m1 × v1) + (m2 × V2)=(m1 + m2) ×V

(3×16) + (6×(-v2) = (3+6) × 0( -V2 because both are moving in opposite directions)

48 - (6 × V2) = 0

48=6 ×V2

therefore, v2 = 8m/s

K.E2=MV²

= 1/2 ×6 x 8²

= 3 × 64

=192

Thus,the kinetic energy will be 192joule

Answer 2

$\bold{\underline{\underline{\huge{\rm{AnsWer:}}}}}$

Kinetic energy of mass 6 kg is 192 Joules.

$\bold{\underline{\underline{\large{\rm{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• A bomb of mass 9 kg.
• The bomb explodes into two pieces

1. $\bold{m_1}$ = 3 kg.
2. $\bold{m_2}$ = 6 kg.

• Velocity of $\bold{m_1}$ = 16 m/sec.
• Initial Velocity (u) = 0 m/sec

1. $\bold{u_1}$ = 0 m/sec
2. $\bold{u_2}$ = 0 m/sec

To FiNd :

• Kinetic energy of mass 6 kg i.e $\bold{m_2}$

SoLuTiOn :

We need to first calculate the velocity of $\bold{m_2}$ using conservation of linear momentum.

$\bold{\sf{Total\:initial\:momentum\:=\:Total\:Final\:Momentum}}$

$\rightarrow$$\bold{\sf{m_1\:\times\:u_1\:+\:m_2\:\times\:u_2\:=\:m_1\:\times\:v_1\:+\:m_2\:\times\:v_2}}$

Block in the values,

$\rightarrow$$\bold{\sf{m_1\:\times\:0\:+\:m_2\:\times\:0\:=\:3\:\times\:16\:+\:6\:\times\:v_2}}$

$\rightarrow$$\bold{\sf{0=48+\:6\:\times\:v_2}}$

$\rightarrow$$\bold{\sf{\:-\:48=\:6\:\times\:v_2}}$

$\rightarrow$$\bold{\sf{\dfrac{-48}{6}}\:=\:v_2}$

$\rightarrow$$\bold{\sf{-8\:=\:v_2}}$

Now, we can calculate the kinetic energy of mass 6 kg using the formula.

FoRmUlA :

$\bold{\huge{\boxed{\tt{\red{K.E\:=\:{\dfrac{1}{2}\:mv^2}}}}}}$

Since we are calculating the kinetic energy of mass 6 kg i.e $\bold{m_2}$ ,we will consider the value of $\bold{v_2}$ i.e - 8 instead of v.

Block in the values,

$\rightarrow$$\bold{\sf{K.E\:=\:{\dfrac{1}{2}\:\times\:6\:\times\:8^2}}}$

$\rightarrow$$\bold{\sf{K.E\:=\:{\dfrac{1}{2}\:\times\:6\:\times\:64}}}$

$\rightarrow$$\bold{\sf{K.E\:=\:{\dfrac{384}{2}}}}$

$\rightarrow$$\bold{\sf{K.E\:=\:192}}$

•°• Kinetic Energy Of Mass 6 kg is 192 Joules.