Question

Find ratio of kinetic energies of two objects A and B of masses 10kg and 50kg respectively but having same momentum?

Answer 1

GIVEN :-

• Mass of object A = 10 kg.
• Mass of object B = 50 kg.

TO FIND :-

• The ratio of kinetic energies [ KE1 : KE2 ]

SOLUTION :-

Since , both the object have same momentum so,

$\implies \sf \: p_1 = p_2$

$\implies \sf \:mv = mu$

$\implies \sf \:50 \times v = 10 \times u$

$\implies \sf \: \dfrac{u}{v} = \dfrac{50}{10}$

$\implies \sf \: \dfrac{u}{v} = \dfrac{5}{1}$

$\implies \underline{ \boxed{\sf \:u\ratio v = 5 \ratio 1}}$

Now According to the question we have to find the ratio of kinetic energies of both the objects so,

Let suppose the velocity of object A be "5x" and the velocity of object B be "x"

$\implies \sf \: \dfrac{KE _1}{KE_2} = \dfrac{ \bigg( \dfrac{mu ^{2} }{2} \bigg)}{ \bigg(\dfrac{mv ^{2} }{2} \bigg)} \\ \implies \sf \: \dfrac{KE _1}{KE_2} = \dfrac{ \bigg( \dfrac{10 \times (x)^{2} }{2} \bigg)}{\bigg(\dfrac{50 \times (5x) ^{2} }{2} \bigg)} \\ \implies \sf \: \dfrac{KE _1}{KE_2} = \dfrac{10 \times u ^{2} }{50 \times v ^{2} } \\ \implies \sf \: \dfrac{KE _1}{KE_2} = \dfrac{1}{5} \times 25 \\ \implies \sf \: \dfrac{KE _1}{KE_2} = \dfrac{5}{1}$

Answer 2

Answer:

Given :-

• Mass of Object A = 10 kg
• Mass of Object B = 50 kg

To Find :-

Ratio of their kinetic energy

Solution :-

We know that

$\checkmark \sf\pink{P_1 = P_2}$

mu = mv

• M is the Mass
• U is the Initial Velocity
• V is the Final Velocity

10 × u = 50 × v

10u = 50v

u/v = 50/10

u/v = 5/1

Now,

Let the Kinetic energies be KE and KE' . Let the velocity be x and 5x

KE/KE' = (mu²/2)/(mv²/2)

KE/KE' = (10 × x²/2)/(50 × 5x²/2)

KE/KE' = (10 × x²)/(50 × x²)

KE/KE' = 10u²/50v²

KE/KE' = 5/1