Question

Kindly refer to attachment!

From the given attachment which of the following option would be correct regards kinetic energy of the ball A and the ball B when they fall on the ground.

Options:

$:\implies \sf K.E_A \: = 3K.E_B \\ \\ :\implies \sf K.E_A \: = K.E_B \\ \\ :\implies \sf 2K.E_A \: = K.E_B \\ \\ :\implies \sf 3K.E_{\dot{A}} \: = K.E_B$



Please explain this to me fully!

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I need correct answer urgently with explanation!...

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Answer 1

Figure:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\framebox(1,3){\sf 6ft}}\put(0.5,3.5){\circle{1}{\sf A}{\sf(4kg)}}\put(3,0){\framebox(1,1){\sf 2ft}}\put(3.5,1.5){\circle{1}{\sf B(12kg)}}\end{picture}$

Concept:-

According to law of conservation of energy the potential energy of the ball at a defined height is equal to the kinetic energy of the ball before hitting the ground.

Solution:-

Case:-1

• $\sf m_A=4kg$
• $\sf h_A=6ft$

Acceleration due to gravity=g=10m/s^2

We know that

$\boxed{\sf P.E=mgh}$

$\\ \sf\longmapsto P.E_A=4\times 10\times 6$

$\\ \sf\longmapsto P.E_A=40\times 6$

$\\ \sf\longmapsto P.E_A=240J$

$\\ \underline{\boxed{\bf{\therefore K.E_A=240J}}}$

Case-2:-

• $\sf m_B=12kg$
• $\sf h_B=2ft$

g=10m/s^2

$\\ \sf\longmapsto P.E_B=12\times 10\times 2$

$\\ \sf\longmapsto P.E_B=120\times 2$

$\\ \sf\longmapsto P.E_B=240J$

$\\ \underline{\boxed{\bf{\therefore K.E_B=240J}}}$

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Comparing both:-

$\\ \sf\longmapsto \dfrac{K.E_A}{K.E_B}=\cancel{\dfrac{240J}{240J}}$

$\\ \sf\longmapsto \dfrac{K.E_A}{K.E_B}=1$

$\\ \sf\longmapsto K.E_A=K.E_B$

$\\ \underline{\boxed{\pmb{\sf{\therefore K.E_A=K.E_B}}}}$

Hope it helps!

Answer 2

THING TO KNOW BEFORE SOLVING:-

We know that:-

Energy the potential energy of the ball at a defined height is equal to the kinetic energy of the ball before hitting the ground.

EXPLANATION:-

$\sf\;m_a=4\;kg\\\\h_a=6\;ft\\\\\boxed{\text{P.E=mgh}}\\g=10\;m./s^2\\\\\rightarrow K.E_a=4\times 10\times 6\\\\\rigtharrow K.E_a=240\;J$

Now,

$\sf\;m_b=12kg\\\\h_b=2\;ft\\\\K.E_B=12\times10\times2\\\\K.E_B=240\; J$

Since the P.E of both are same

So we can say,

$\boxed{\underline\bold\huge{K.E_a=K.E_b}}$

So opt-B is the required answer,

CHEERS !!