Let's solve the problem step by step:

Step 1: Determine the initial kinetic energy (K.E) of the colliding body before the collision.
The initial kinetic energy of a body is given by the formula: K.E = (1/2)mv^2, where m is the mass of the body and v is its velocity.
In this case, the mass of the colliding body is m and its velocity is V. Therefore, the initial kinetic energy is K.E1 = (1/2)mV^2.

Step 2: Determine the initial kinetic energy (K.E) of the second body before the collision.
The second body is initially at rest, so its initial kinetic energy is zero.

Step 3: Determine the total initial kinetic energy before the collision.
The total initial kinetic energy is the sum of the initial kinetic energies of both bodies. Therefore, K.E_total = K.E1 + K.E2 = (1/2)mV^2 + 0 = (1/2)mV^2.

Step 4: Determine the final kinetic energy (K.E) of the colliding body after the collision.
In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Therefore, K.E_total = K.E1' + K.E2', where K.E1' and K.E2' are the final kinetic energies of the colliding body and the second body, respectively.

Step 5: Determine the final kinetic energy (K.E) of the second body after the collision.
Since the second body was initially at rest, its final kinetic energy is given by the formula: K.E2' = (1/2)(2m)(0)^2 = 0.

Step 6: Determine the final kinetic energy (K.E) of the colliding body after the collision.
Using the equation K.E_total = K.E1' + K.E2', we can substitute the values and solve for K.E1': (1/2)mV^2 = K.E1' + 0.
Therefore, K.E1' = (1/2)mV^2.

Step 7: Determine the ratio of the initial and final kinetic energies of the colliding body.
The ratio of K.E1 to K.E1' is given by: K.E1 / K.E1' = [(1/2)mV^2] / [(1/2)mV^2] = 1.

Step 8: Simplify the ratio.
The ratio of the initial and final kinetic energies of the colliding body is 1:1.

Therefore, the correct answer is not provided in the given options.

Question

Let's solve the problem step by step:

Step 1: Determine the initial kinetic energy (K.E) of the colliding body before the collision.
The initial kinetic energy of a body is given by the formula: K.E = (1/2)mv^2, where m is the mass of the body and v is its velocity.
In this case, the mass of the colliding body is m and its velocity is V. Therefore, the initial kinetic energy is K.E1 = (1/2)mV^2.

Step 2: Determine the initial kinetic energy (K.E) of the second body before the collision.
The second body is initially at rest, so its initial kinetic energy is zero.

Step 3: Determine the total initial kinetic energy before the collision.
The total initial kinetic energy is the sum of the initial kinetic energies of both bodies. Therefore, K.E_total = K.E1 + K.E2 = (1/2)mV^2 + 0 = (1/2)mV^2.

Step 4: Determine the final kinetic energy (K.E) of the colliding body after the collision.
In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Therefore, K.E_total = K.E1' + K.E2', where K.E1' and K.E2' are the final kinetic energies of the colliding body and the second body, respectively.

Step 5: Determine the final kinetic energy (K.E) of the second body after the collision.
Since the second body was initially at rest, its final kinetic energy is given by the formula: K.E2' = (1/2)(2m)(0)^2 = 0.

Step 6: Determine the final kinetic energy (K.E) of the colliding body after the collision.
Using the equation K.E_total = K.E1' + K.E2', we can substitute the values and solve for K.E1': (1/2)mV^2 = K.E1' + 0.
Therefore, K.E1' = (1/2)mV^2.

Step 7: Determine the ratio of the initial and final kinetic energies of the colliding body.
The ratio of K.E1 to K.E1' is given by: K.E1 / K.E1' = [(1/2)mV^2] / [(1/2)mV^2] = 1.

Step 8: Simplify the ratio.
The ratio of the initial and final kinetic energies of the colliding body is 1:1.

Therefore, the correct answer is not provided in the given options.

Knowee AI · Accepted Answer