Question

The momentum of a body of mass 15 kg is 50 kg m/s. Find its kinetic energy.​

Answer 1

Given :

• Momentum of a body of mass 15 kg = 50 kgm/s

To Find :

• The Kinetic energy

Solution :

The relation between Momentum and kinetic energy is given by ;

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

Here,

• P is momentum

• KE is kinetic energy

• m is mass

We have,

P = 50 kgm/s

m = 15 kg

Substituting the values we have ;

$\\ : \implies \sf \: KE = \dfrac{(50 \: kgm {s}^{ - 1} )^2}{2(15 \: kg)}$

$\\ : \implies \sf \:KE = \dfrac{50 \: kgm {s}^{ - 1} \times 50 \: kgm {s}^{ - 1} }{30 \: kg}$

$\\ : \implies \sf \: KE = \dfrac{50 \times 50 \: {kg}^{2} {m}^{2} {s}^{ - 2} }{30 \: kg}$

$\\ : \implies \sf \:KE = \dfrac{2500 \: {kg}^{2} {m}^{2} {s}^{ - 2} }{30 \: kg}$

$\\ : \implies \sf \:KE = \dfrac{2500 \: kg {m}^{2} {s}^{ - 2} }{30}$

$\\ : \implies \sf \:KE = 83.33 \: kg {m}^{2} {s}^{ - 2}$

$\\ : \implies{\underline{\boxed{\pink{\sf{KE ={\mathfrak{ 83.33 \: {\sf{J}}}}}}}}} \: \bigstar$

Hence,

The Kinetic energy of the given body is 83.33J.

Answer 2

Given -

• Momentum of a body is 50 kg m/s
• Mass of a body is 15 kg

⠀

To find -

• It's kinetic energy

⠀

Solution -

$\longmapsto \sf \: KE = \dfrac{(50 \: kgm {s}^{ - 1} )^2}{2(15 \: kg)}$

⠀

$\longmapsto \sf \:KE = \dfrac{50 \: kgm {s}^{ - 1} \times 50 \: kgm {s}^{ - 1} }{30 \: kg}$

⠀

$\longmapsto \sf \: KE = \dfrac{50 \times 50 \: {kg}^{2} {m}^{2} {s}^{ - 2} }{30 \: kg}$

⠀

$\longmapsto \sf \:KE = \dfrac{2500 \: {kg}^{2} {m}^{2} {s}^{ - 2} }{30 \: kg}$

⠀

$\longmapsto \sf \:KE = \dfrac{2500 \: kg {m}^{2} {s}^{ - 2} }{30}$

⠀

$\longmapsto \sf \:KE = 83.33 \: kg {m}^{2} {s}^{ - 2}$

⠀

$\longmapsto{\underline{\boxed{\purple{\sf{KE = 83.33 \: J}}}}}$

⠀

Hence, the kinetic energy is 83.33 Joule.