Question

An object of mass m and velocity v has kinetic energy= 200J.find the new kinetic energy of the mass of an object becomes double and the velocity remains the same

Answer 1

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

We are Given ,

Mass of object = m

velocity of the object = v

Kinetic Energy (K.E) = 200 J

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Solution :-

Formula for Kinetic Energy is :-

$\huge{\boxed{\boxed{\orange{\sf{K.E \: = \: \frac{1}{2}mv^2}}}}}$

If,

K.E = 200 J

Then,

$\huge{\implies}{\boxed{\sf{200 \: = \: \frac{1}{2}mv^2}}---(1)}$

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A.T.Q,

Mass becomes twice then

m' = 2m (new mass)

K.E' = New Kinetic energy

$\huge{\implies}{\sf{K.E' \: = \: \frac{1}{2}m'v^2}}$

Put Value of m'

$\Large{\sf{K.E' \: = \: \frac{1}{2}2mv^2}}$

$\Large{\sf{K.E' \: = \: \frac{1}{2}mv^2(2)}}$

Put Value of K.E or (1)

We get,

$\Large{\sf{K.E'\: = \: K.E \: \times \: 2}}$

$\Large{\sf{K.E' \: = \: 200 \: \times \: 2}}$

$\huge{\implies}{\boxed{\boxed{\green{\sf{K.E' \: = \: 400 \: J }}}}}$

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∴ New Kinetic Energy will be 400 J

Answer 2

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Kinetic Energy is the work done by an object by the virtue of its motion

From the Question,

• Mass of the object = m Kg

• Initial Kinetic Energy = 200 J

We Know that,

$\purple{\huge{\underline{ \boxed{\sf{K= \frac{1}{2}mv {}^{2}} }}}}$

Now,

$\implies \large{\displaystyle{\sf{{v}^{2} = \frac{400}{m}}}...............(1)}}$

The mass of the object is doubled » Mass = 2m

Velocity remains the same

Putting the values,we get:

$\sf{{K}_{f} = \frac{1}{2}.2\cancel{m}.\frac{400}{\cancel{m}}} \ \ \ [Using (1)] \\ \\ \implies \: \sf{{K}_{f} = (400) J} \\ \\ \huge{\implies \: \underline{\boxed{\sf{{K}_{f}= 400 \: J }}}}$

Thus,the final Kinetic Energy of the object would be 400 Joules