Question

One object has a mass of 1 kg and another object has a mass of 3 kg. If the speeds are the same, which of the following is true about their kinetic energy?
Their masses are the same.
The object with a higher mass has three times the kinetic energy of the less massive object.
It is impossible to determine without the speeds.
The object with a smaller mass has a greater kinetic energy than the object with a higher mass.

Answer 1

Answer:

The object with a higher mass has three times the kinetic energy of the less massive object.

We know that K.E.= 1/2 mv²

mass of first object = 1kg

speed = v

So K.E. = 1/2mv²

= 1/2 × (1) × v²

=

$\: \: \: \: \: \: \: \: \: = \frac{1}{2} {v}^{2}$

Now the mass of second body = 3kg

speed = v

So K.E. = 1(3)v²/2

=

$\: \: \: \: \: \: \: \: \: = \: \: \frac{3}{2} {v}^{2}$

now

K.E of first / KE of 2nd

$\frac{1}{2} {v}^{2} \div \frac{3}{2} {v}^{2}$

$\frac{ \frac{ke \: of \: first \: }{ - - - - - - - - - - -} }{ \frac{ke \: of \: 2nd}{} } = \frac{ \frac{1}{ - -} }{ 3 } \\ \\ so \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ 3(ke \: of \: first \:) = ke \: of \: 2nd$