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Question

(i) What do you understand by the kinetic energy of a body? (ii) A body is thrown vertically upwards. Its velocity goes on decreasing. What happens to its kinetic energy as its velocity becomes zero? ā(iii) A horse and a dog are running with the same speed. If the weight of the horse is ten times that of the dog, what is the ratio of their kinetic energies?

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Solution

(i) The energy possessed by a body by virtue of its motion is known as the kinetic energy of the body. If the mass of a body is 'm' and it is moving with a speed 'v', then the kinetic energy of the body = $\frac{1}{2}m{v}^{2}$ (ii) When a body is thrown in an upward direction, its velocity decreases continuously but its potential energy goes on increasing. As the body reaches a maximum height, the kinetic energy gradually gets converted into potential energy. At the highest point where the velocity of the body becomes zero, the potential energy of the body becomes maximum. Because all of the kinetic energy gets converted into potential energy. (iii) Let the speed of the horse and the dog = v If the mass of the dog = m Then the mass of the horse = 10m The ratio of kinetic energies of the horse and the dog = $\frac{\left(K.E.{\right)}_{\mathrm{Horse}}}{\left(K.E.{\right)}_{\mathrm{Dog}}}=\frac{\frac{1}{2}\left(10m\right){v}^{2}}{\frac{1}{2}m{v}^{2}}=\frac{10}{1}$ Hence, the ratio of their kinetic energies is 10:1.

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