Chapter 10 Work and Energy Questions-03
Questions
1. What is the kinetic energy of an object?
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Answer
The energy possessed by a body by virtue of its motion is termed mechanical energy or kinetic energy. Every moving object possesses mechanical energy. A body uses mechanical energy to try to work. The kinetic energy of the hammer is employed in driving a nail into a log of wood, the mechanical energy of air is employed to run wind mills, etc.
2. Write an expression for the kinetic energy of an object.
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Answer
If a body of mass $m$ is moving with a speed $v$, then its K.E. $E_k$ is given by the expression,
$\mathrm{E}_{\mathrm{k}}=1 / 2 \mathrm{~m} \mathrm{v}^2$
Its SI unit is Joule (J).
3. The kinetic energy of an object of mass, $m$ moving with a velocity of $5 m s^{-1}$ is $25 J$. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?
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Answer
Given
K.E. of the object $=25 \mathrm{~J}$
Velocity of the object (v) $=5 \mathrm{~m} / \mathrm{s}$
$ \begin{aligned} & \text { K.E. }=(1 / 2) \mathrm{mv}^2 \\ & 25=(1 / 2) \mathrm{m}(5)^2 \\ & 50=25 \mathrm{x} \mathrm{m} \\ & \mathrm{m}=50 / 25 \\ & \mathrm{~m}=2 \mathrm{~kg} \end{aligned} $
Now, when velocity is doubled
$ \begin{aligned} & \mathrm{v}=10 \mathrm{~m} / \mathrm{s} \\ & \mathrm{m}=2 \mathrm{~kg} \\ & \text { K.E. }=(1 / 2) \times 2 \times(10)^2 \\ & \text { K.E. }=10^2 \\ & \text { K.E. }=100 \mathrm{~J} \end{aligned} $
When velocity is increased three times, then
$ \begin{aligned} & \mathrm{v}=15 \mathrm{~m} / \mathrm{s} \\ & \mathrm{m}=2 \mathrm{~kg} \\ & \text { K.E. }=(1 / 2) \times 2 \times(15)^2 \end{aligned} $
$\begin{aligned} & \text { K.E. }=(15)^2 \\ & \text { K.E. }=225 \mathrm{~J}\end{aligned}$
