Question

The momentum of a bullet of mass 20 g fired from a gun is 10 kg.m/s. The

kinetic energy of this bullet in kJ will be :

(a) 5 (b) 1.5

(c) 2.5 (d) 25​

Answer 1

Given :

• Mass of the bullet is 20 g

• Momentum of the bullet is 10 kgm/s

To find :

• The Kinetic energy of the bullet in KJ

Solution :

The relation between g and kg is given is 1g = 0.001 kg

Then mass of the bullet = 20g = 0.02 kg

The relation between kinetic energy and momentum of a body is given by ,

$\star \boxed{ \purple{ \sf{KE = \dfrac{P^2}{2m}}}}$

Where ,

• KE is kinetic energy
• P is momentum
• m is mass

We have ,

• P = 10 kgm/s
• m = 0.02 kg

By substituting the values ,

$\\ : \implies \sf \: KE = \dfrac{(10 )^2}{2(0.02 \: )} \\ \\ \\ : \implies \sf \: KE = \dfrac{100 }{0.04 \: } \\ \\ \\ : \implies \sf \:KE = 2500 \: \: J$

The relation between J and KJ is 1J = 0.001 J

$: \implies \sf 2500 \: J= 2500 \times 0.001 \: KJ \\ \\ \\ : \implies \sf \: 2500 \: J= 2.5 \: KJ$

The Kinetic energy of the bullet in KJ is 2.5 KJ.

Hence , Option(3) is the required answer.

Answer 2

Explanation:

Given :

Mass of the bullet is 20 g

Momentum of the bullet is 10 kgm/s

To find :

The Kinetic energy of the bullet in KJ

Solution :

The relation between g and kg is given is 1g = 0.001 kg

Then mass of the bullet = 20g = 0.02 kg

The relation between kinetic energy and momentum of a body is given by ,

\star \boxed{ \purple{ \sf{KE = \dfrac{P^2}{2m}}}}⋆

KE=

2m

P

2

Where ,

KE is kinetic energy

P is momentum

m is mass

We have ,

P = 10 kgm/s

m = 0.02 kg

By substituting the values ,

\begin{gathered} \\ : \implies \sf \: KE = \dfrac{(10 )^2}{2(0.02 \: )} \\ \\ \\ : \implies \sf \: KE = \dfrac{100 }{0.04 \: } \\ \\ \\ : \implies \sf \:KE = 2500 \: \: J \end{gathered}

:⟹KE=

2(0.02)

(10)

2

:⟹KE=

0.04

100

:⟹KE=2500J

The relation between J and KJ is 1J = 0.001 J

\begin{gathered} : \implies \sf 2500 \: J= 2500 \times 0.001 \: KJ \\ \\ \\ : \implies \sf \: 2500 \: J= 2.5 \: KJ\end{gathered}

:⟹2500J=2500×0.001KJ

:⟹2500J=2.5KJ

The Kinetic energy of the bullet in KJ is 2.5 KJ.

Hence , Option(3) is the required answer.