A body of mass 5 kg is moving with a velocity 10 ms-1. Find its kinetic energy. Find the ratio of initial kinetic and final kinetic energy if (a) its mass is doubled, (b) its velocity is made three times.
Answers
The ratio of initial kinetic and final kinetic energy is 1 : 180.
Answer:
The ratio of final to initial kinetic energies
a) If the mass is doubled, the ratio will be 1 : 2.
b) If the velocity is made three times, the ratio will be 1 : 9
Explanation:
Mass of the body, m = 5 Kg
Velocity of the body, v = 10 m/s
The kinetic energy of the body, K.E₁ = 1/2 (mv²)
= 1/2 (5 × 10²)
= 250 J
a) If the mass is doubled
New mass of the body, m = 2× 5 = 10 Kg
The kinetic energy of the body, K.E₂ = 1/2 (mv²)
= 1/2 (10 × 10²)
= 500 J
The ratio of initial to the final kinetic energy of the body will be;
K.E₁ : K.E₂ = 250 : 500 = 1 : 2
b) If the velocity of the body is tripled
New velocity of the body, v = 3 × 10 = 30 m/s
The kinetic energy of the body, K.E₃ = 1/2 (mv²)
= 1/2 (5 × 30²)
= 2250 J
The ratio of initial to the final kinetic energy of the body will be;
K.E₁ : K.E₃ = 250 : 2250 = 1 : 9