Question

A body of mass 40 kg has kinetic energy 500 J. The magnitude (numerical value) of the momentum of the body is

Answer 1

☯ Momentum = 200 kgm/s

Given ,

• Kinetic energy = 500J
• Mass of body = 40kg

We need to find ,

• Momentum of the body = ?

Now , firstly finding velocity of the body

♦ K.E = 1/2 mv²

⇒ 500 = 1/2 × 40 × v²

⇒ 500 × 2 = 40 × v²

⇒ 1000 = 40v²

⇒ v² = 1000/40

⇒ v² = 25

⇒ v = √25

⇒ Velocity = 5 m/s

Now , finding momentum

♦ Momentum = Mass × Velocity

→ p = 40 × 5

→ Momentum = 200 kgm/s

Answer 2

Answer:

• Mass (m) = 40 kg
• Kinetic Energy = 500 J
• Momentum of Body (p) = ?

$\underline{\bigstar\:\textsf{Kinetic Energy of a body is equal to :}}$

$:\implies\sf K.E.={}^{1}\!/{}_{2}\:mv^2\\\\\\:\implies\sf 500 ={}^{1}\!/{}_{2} \times 40 \times v^2\\\\\\:\implies\sf 500 = 20 \times v^2\\\\\\:\implies\sf \bcancel\dfrac{500}{20} = v^2\\\\\\:\implies\sf 25 = v^2\\\\\\:\implies\sf \sqrt{25} = v\\\\\\:\implies\sf \sqrt{5 \times 5} = v\\\\\\:\implies\sf v = 5 \:m/s$

$\rule{200}{1}$

$\underline{\bigstar\:\textsf{Momentum of the body is equal to :}}$

$\dashrightarrow\sf \: \:Momentum=Mass \times Velocity\\\\\\\dashrightarrow\sf \: \: p=40 \:kg \times 5 \:m/s\\\\\\\dashrightarrow\sf \: \: p=200 \:kgm {s}^{ - 1}$

⠀

$\therefore\:\underline{\textsf{Momentum of the body is equal to \textbf{200 kgms ^{ - 1} }}}.$