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Is it true that the change in kinetic energy is equal to the work done by the force on the body?

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True

False

answer is A.

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Detailed Solution

The above statement is true.
The kinetic energy of the body is equal to,

K . E = \frac{1}{2} mv²

m = mass

and

v = velocity

The work done is equal to,

\Rightarrow W = F . s

Here,

W = work, F = force

Third equation of motion,

\Rightarrow v² - u² = 2 a

s
Here,

v =

final velocity

u =

Initial velocity

a =

acceleration

s =

displacement

\Rightarrow s = \frac{v² - u²}{2 a}

…………………………………….

(1)

Also, force is equal to,

\Rightarrow F = ma

………………………………………

(2)

Using eq

(1)

and eq

(2)

in the formula of work done.

\Rightarrow W = F . s

\Rightarrow W = ma \times \frac{v^{2} - u^{2}}{2 a}

\Rightarrow W = m \times \frac{v^{2} - u^{2}}{2}

\Rightarrow W = \frac{1}{2} m (v² - u²)

So, the change in kinetic energy is equal to the work done by the force on the body.

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