Question

The kinetic energy of a body will become eight times,if__________________. *
1 point
both the mass and the velocity are doubled
its mass is quadrupled
its velocity is quadrupled
both the mass and velocity are quadrupled

Answer 1

Answer:Kinetic energy is directly proportional to mass and velocity. Since mass is directly proportional to K.E and K.E is directly proportional to the square of velocity the kinetic energy becomes eight times.

Explanation:

Answer 2

The kinetic energy becomes 8 times, if the mass and velocity are doubled (A).

Given:

4 assumptions.

To find:

Using which assumption, the kinetic energy of the body becomes 8 times.

Explanation:

• Kinetic energy of a body is the energy possessed by a body by virtue of its velocity.

• Any body that has a non zero mass and is running with certain velocity possess kinetic energy.

• For example, a leaf falling from top of a tree as well as a bullet fired from a gun both have kinetic energy as both have a non zero mass and have gained velocity due to some or the other reasons.

• Mathematically, Kinetic energy is given by

                               $KE=\frac{1}{2}mv^{2}$

Solution:

According to the question,

Step 1

Both mass and velocity are doubled.

We have , $m=2m$    ;   $v=2v$

$KE'=\frac{1}{2}(2m)(2v)^{2}$

        $=(8)\frac{1}{2} mv^{2}$

$KE'=8KE$

Hence, the kinetic energy becomes 8 times if we double the mass and velocity of the objects.

Step 2

If mass is quadrupled

We have $m=4m$    ;  $v=v$

$KE'=\frac{1}{2}(4m)v^{2}$

        $=(4)\frac{1}{2}mv^{2}$

$KE'=4KE$

Here, the kinetic energy gets quadrupled.

Step 3

If mass is quadrupled.

We have,  $m=m$    ; $v=4v$

$KE'=\frac{1}{2}(m)(4v)^{2}$

        $=(16)\frac{1}{2}mv^{2}$

$KE'=16KE$

Here, the kinetic energy becomes 16 times the original.

Step 4

Both the velocity and mass are quadrupled.

We have,  $m=4m$     ;  $v=4v$

$KE'=\frac{1}{2}(4m)(4v)^{2}$

        $=(64)\frac{1}{2}mv^{2}$

$KE'=64KE$

Here, the kinetic energy becomes 64 times.

Final answer:

Hence, the kinetic energy becomes 8 times only when the mass and velocity are doubled (A).