Question

Kinetic energy of a body is 75000J. If the mass of the body is 60kg, then its momentum is​

Answer 1

GIVEN :-

• Kinetic energy ( E_k ) = 75000 J.
• Mass of the body ( m ) = 60 kg.

TO FIND :-

• The momentum of the body ( p ).

SOLUTION :-

As we know that,

$\boxed{ \implies \sf \: E_{k} = \dfrac{1}{2} mv ^{2} }$

Substitute all the given values,

$\implies \sf \: 75000 = \dfrac{1}{2} \times 60 \times v ^{2}$

$\implies \sf \: \dfrac{75000 \times 2}{60} = v ^{2}$

$\implies \sf \: \dfrac{150000}{60} = v ^{2}$

$\implies \sf \: \dfrac{5000}{2} = v ^{2}$

$\underline{ \underline{\implies \sf \:v = \sqrt{ \dfrac{5000}{2} } \: ms ^{ - 1} }}$

Now as we know that,

$\implies \sf \: p = mv$

$\implies \sf \: p =60 \: kg \: \times \sqrt{ \dfrac{5000}{2} } ms ^{ - 1}$

$\implies \sf \: p = \sqrt{ \dfrac{5000 \times 3600}{2} }$

$\implies \sf \: p = \sqrt{ \dfrac{18000000}{2} } kg.ms ^{ - 1}$

$\implies \sf \: p = \sqrt{9000000} \: kg.ms ^{ - 1}$

$\implies \sf \: p = 3000 \: kg.ms ^{ - 1}$

$\boxed{\implies \sf \: p = 3 \times 10 ^{3} \: kg.ms ^{ - 1} }$

Answer 2

Given :-

Kinetic energy = 75000 J

Mass = 60 kg

To Find :-

Momentum

Solution :-

We know that

KE = 1/2 mv²

75000 = 1/2 × 60 × v²

75000 = 30v²

75000/30 = v²

7500/3 = v²

2500 = v²

√(2500) = v

500 = v

Now

Momentum = mv

p = mv

p = 60 × 500

p = 30000 kg m/s