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A stationary particle explodes into two particles of masses 300 g and 250 g which movein opposite directions with velocities v1m/s and v2m/s respectively. Find the ratio oftheir kinetic energies

Question

A stationary particle explodes into two particles of masses 300 g and 250 g which movein opposite directions with velocities v1m/s and v2m/s respectively. Find the ratio oftheir kinetic energies

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Solution

The kinetic energy of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

For the first particle with mass 300g and velocity v1, the kinetic energy (KE1) is:

KE1 = 1/2 * 300g * (v1)^2

For the second particle with mass 250g and velocity v2, the kinetic energy (KE2) is:

KE2 = 1/2 * 250g * (v2)^2

The ratio of their kinetic energies (KE1/KE2) is therefore:

KE1/KE2 = (1/2 * 300g * (v1)^2) / (1/2 * 250g * (v2)^2)

The 1/2 in both the numerator and denominator cancels out, leaving:

KE1/KE2 = (300g * (v1)^2) / (250g * (v2)^2)

This simplifies to:

KE1/KE2 = (300/250) * ((v1)^2 / (v2)^2)

Therefore, the ratio of their kinetic energies depends on the squares of their velocities and their masses.

This problem has been solved

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