Question

the kinetic energy of two bodies of same mass are in the ratio 1 ratio 4 the ratio of linear momentum of these bodies in is​

Answer 1

MK10

MK10Expert

1. We know that,

Kinetic Energy= 1/2mv²

K.E= mv/2×v--------(1)

Now

p(momentum)= m×v

v=p/m-------------(2)

Putting (2) in (1)

mv/2×p/m= K.E

p/2×p/m= K.E

p²/2m= K.E

Let the mass of one object be m and momentum p.

Let the mass of another object be m' and momentum p'.

Kinetic Energy of Object 1= p²/2m

Kinetic Energy of Object 2= p'²/2m'

Kinetic Energy of Object 1/Kinetic Energy of

Object 2= 4/1

Kinetic Energy of Object 1/Kinetic Energy of

Object 2= p²/2m÷p'²/2m'

As p= p’, p²=p'²

4/1=2m/2m’

4/1=m/m'

m:m'= 4:1

2. Here, we will use the formula of m1u1+m2u2= m1v1+m2v2

Here, m1u1+m2u2= (m1+m2)(v)= mv

mv= m1v1+m2v2

As Object with mass m1 is stationary after explosion,

mv= m2v2

m2= m-m1= m-m/4= 3m/4

mv= (3m/4)(v2)

(mv)(4)/3m= v2

4mv/3m=v2

4v/3 m/s = v2

Hope it helps! Please mark it as 'Brainliest'!

Answer 2

GIVEN :-

• Ratio of kinetic energies of two bodies of same mass is given as 1 : 4

TO FIND :-

• Ratio of linear momentum of the two bodies

SOLUTION :-

Relation between momentum and kinetic energy is given by ,

$\large {\underline {\boxed {\bigstar {\sf{ KE = \frac{ {P}^{2} }{2m} }}}}}$

Where ,

• KE is kinetic energy
• P is momentum
• m is mass of the body

We have ,

• (KE)₁ : (KE)₂ = 1 : 4
• masses are equal

$\implies \sf \: \frac{KE_1}{KE_2} = \frac{1}{4} \\ \\ \implies \sf \: \dfrac{ \dfrac{ {(P_1)}^{2} }{2m} }{ \dfrac{(P_2){}^{2} }{2m} } = \frac{1}{4} \\ \\ \implies \sf \: \frac{(P_1){}^{2} \times 2m}{(P_2) {}^{2} \times 2m } = \frac{1}{4} \\ \\ \implies \sf \: \frac{(P_1){}^{2} \times \cancel{2m} }{(P_2) {}^{2} \times \cancel{2m}} = \frac{1}{4} \\ \\ \implies \sf \: \frac{(P_1) {}^{2} }{(P_2){}^{2} } = \frac{1}{4} \\ \\ \implies \sf \: \frac{P_1}{P_2} = \sqrt{ \frac{1}{4} }$

$\implies \sf \: \frac{P_1}{P_2} = \sqrt{\frac{(1) \times (1)}{(2) \times (2)} } \\ \\ \implies \sf \: \frac{P_1}{P_2} = \sqrt{ \frac{(1) {}^{2} }{(2) {}^{2} } } \\ \\ \implies \sf \: \frac{P_1}{P_2} = \frac{1}{2} \\ \\ \implies {\underline {\boxed {\blue { {\sf {\: P_1 : P_2 = 1 : 2}}}}}}$

∴ The ratio of the momentum of the given bodies is 1 : 2