Which object has the least amount of kinetic energy? 1. mass and velocity are each reduced by one-half, 2. mass is reduced by one-half, and velocity is doubled, 3. mass is doubled and velocity is reduced by one-half, 4. mass and velocity are each doubled.

Option (1)

Explanation:

The energy possessed by the object by virtue of its motion is called kinetic energy.

The formula for the kinetic energy is given by

K = 1/2 mv^2

1. Now the mass is reduced to half and velocity also reduced to half.

The new kinetic energy

K' = 1/2 × m/2 × v^2/4

K' = K/8

2. Now mass is half and velocity is doubled.

K' = 1/2 × m/2 × 4v^2

K' = 2K

3. Now mass is double and velocity is half.

K' = 1/2 × 2m × v^/4

K' = K/2

4. Now mass and velocity both are doubled.

K' = 1/2 × 2m × 4v^2

K' = 8K

So, kinetic energy is least in case 1.

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