Question

The momentum of a bullet of mass 10 g fired from a gun is 1 kg.m/s. the kinetic energy of the bullet will be
a) 6 K J
b) 50 J
c) 5 KJ
d) 60 J​

Answer 1

Given:-

→ Mass of the bullet = 10g

→ Momentum of the bullet = 1 kg.m/s

To find:-

→ Kinetic energy of the bullet

Solution:-

Firstly, let's convert the mass of the bullet

from g to kg.

=> 1g = 0.001kg

=> 10g = 10(0.001)

=> 0.01kg

Now, we know that :-

∵ K.E. = ½mv²

=> K.E. = ½mv² × m/m

=> K.E. = (mv)²/2m

∴ K.E. = p²/2m

Where :-

• K.E. is the kinetic energy of the body.

• p is momentum of the body.

• m is the mass of the body.

By substituting values, we get :-

=> K.E. = (1)²/(2×0.01)

=> K.E. = 1/0.02

=> K.E. = 50 J

Thus, kinetic energy of the bullet is 50 J [Option.b]

Some Extra Information:-

❒ Kinetic energy is the energy

possessed by a body beacuse of

its motion.

❒ K.E. = ½mv²

This expression shows that K.E. of a body depends on two factors :-

(a) Mass [ K.E. ∝ m ]

(b) Velocity [ K.E. ∝ v² ]

Answer 2

Given,

mass of bullet = 10 g = 10^(-2) kg

momentum (p) = 1 kg.m/s

$\boxed{K.E.=\frac{p²}{2m}}$

$\sf \: K.E=\frac{1²}{2×10^{-2}}$

$\sf \: K.E = \frac{10²}{2}=50$

$\boxed{ \sf \:K.E \: of \: the \: bullet \: will \: be \: 50 \: J }$