Physics, asked by tanmayd2007, 4 days ago

1) The Rinetic energy of an objec of mass (m) moving with a velocity of smo u 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 time?​

Answers

Answered by Aeryxz
6

\underline{\underline{\bigstar\;\frak{Corrected\; question\;:}}}

  • The kinetic energy of an object of mass, m moving with a velocity of 5 ms-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?

\underline{\underline{\bigstar\;\frak{Solution\;:}}}

  • Here, we are given that the kinetic energy of an object of mass ( m ) moving with a velocity of 5 ms-¹ is 25 J. We are asked to calculate it's kinetic energy if:

\quad\qquad Velocity is doubled.

\quad\qquad Velocity is increased three times.

» We've to calculate the kinetic energy of the object for the given situation. We know, the kinetic energy is calculated by:

\qquad\star\; \underline{\boxed{\pmb{\frak{Kinetic\; energy=\dfrac{1}{2}\times m\times {v}^{2}}}}}

where:

  • m is the mass of the object.
  • v is the velocity of object.
  • Given kinetic energy and velocity are 25 J and 5 ms-¹.

\:

\underline{\dag\; \frak{SubstitutinG\; the\; values\; in\; FormulA\;:}}

\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{2}\times m\times {v}^{2}}

\\\longrightarrow\quad\sf{25=\dfrac{1}{2}\times m\times {5}^{2}}

\\\longrightarrow\quad\sf{m=\dfrac{\cancel{25}\times 2}{\cancel{25}}}

\\\longrightarrow\quad\sf{m=2}

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

Case ( I ): Velocity is doubled.

  • Value of mass will remain same (2 kg) & the velocity will be 2 times the velocity in given question.

\\\longrightarrow\quad\sf{Kinetic\; energy=\dfrac{1}{2}\times m\times {v}^{2}}

\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{\cancel{\;2}}\times \cancel{\;2}\times {2\times 5}^{2}}

\\\longrightarrow\quad\sf{Kinetic\: energy={10}^{2}}

\\\longrightarrow\quad\underline{\boxed{\pmb{\frak{Kinetic\: energy=100\; J}}}}

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

★ Case ( II ): Velocity is increased three times.

  • Value of mass will remain same (2 kg) & the velocity will be 3 times the velocity given in the question.

\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{2}\times m\times {v}^{2}}

\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{\cancel{\; 2}}\times \cancel{\; 2}\times {3\times 5}^{2}}

\\\longrightarrow\quad\sf{Kinetic\: energy={15}^{2}}

\\\longrightarrow\quad\underline{\boxed{\pmb{\frak{Kinetic\: energy=225\; J}}}}

Answered by Anonymous
0

Solution :

Here, we are given that the kinetic energy of an object of mass ( m ) moving with a velocity of 5 ms-¹ is 25 J. We are asked to calculate it's kinetic energy if :

\quad\qquad ▪ Velocity \:  \:  is \:  \:  doubled. \\  \\ \quad\qquad ▪ Velocity \:  \:  is \:  \:  increased \:  \:  three  \:  \: times.

» We've to calculate the kinetic energy of the object for the given situation. We know, the kinetic energy is calculated by:

\qquad\; \underline{\boxed{\pmb{\frak{Kinetic\; energy=\dfrac{1}{2}\times m\times {v}^{2}}}}}

where :

m is the mass of the object.

v is the velocity of object.

Given kinetic energy and velocity are 25 J and 5 ms-¹.

Substituting the values in formula :

\begin{gathered}\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{2}\times m\times {v}^{2}} \end{gathered}  \\  \\ \begin{gathered}\\\longrightarrow\quad\sf{25=\dfrac{1}{2}\times m\times {5}^{2}} \end{gathered} \\  \\\begin{gathered}\\\longrightarrow\quad\sf{m=\dfrac{\cancel{25}\times 2}{\cancel{25}}} \end{gathered}

m = 2

⠀⠀

Case ( I ) : Velocity is doubled.

Value of mass will remain same (2 kg) & the velocity will be 2 times the velocity in given question ,

\begin{gathered}\\\longrightarrow\quad\sf{Kinetic\; energy=\dfrac{1}{2}\times m\times {v}^{2}} \end{gathered}  \\  \\ \begin{gathered}\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{\cancel{\;2}}\times \cancel{\;2}\times {2\times 5}^{2}} \end{gathered} \\  \\\begin{gathered}\\\longrightarrow\quad\sf{Kinetic\: energy={10}^{2}} \end{gathered}

Kinetic energy = 100 J .

Case ( II ) : Velocity is increased three times.

Value of mass will remain same (2 kg) & the velocity will be 3 times the velocity given in the question,

\begin{gathered}\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{2}\times m\times {v}^{2}} \end{gathered} \\  \\\begin{gathered}\\\longrightarrow\quad\sf{Kinetic\: energy=\dfrac{1}{\cancel{\; 2}}\times \cancel{\; 2}\times {3\times 5}^{2}} \end{gathered}  \\  \\\begin{gathered}\\\longrightarrow\quad\sf{Kinetic\: energy={15}^{2}} \end{gathered}

Kinetic energy = 225 J .

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