Question

two objects whose masses are in the ratio of 2:3 are moving with speed in the ratio of 4:5. calculate the ratio of their Kinetic energies

Answer 1

$\large\underline\bold{Given:\longrightarrow}$

Ratio of masses of the two objects = 2 : 3
Ratio of the speeds of the two objects = 4 : 5

$\large\underline\bold{To~Find:\longrightarrow}$

Ratio of the kinetic energy possessed by the two objects

$\large\underline\bold{Solution:\longrightarrow}$

Let the masses, m1 and m2 be 2x and 3x respectively.

Let the speeds( or velocity as direction doesn't change ), v1 and v2 be 4y and 5y.

We know that,

Kinetic energy of an object = 1/2 * m * v ^ 2

Hence,

Ratio of the kinetic energy of two objects,
= ( 1/2 * m1 * v1 ^ 2 ) / ( 1/2 * m2 * v2 ^ 2 )
= ( 1/2 * 2x * 4y ^ 2 ) / ( 1/2 * 3x * 5y ^ 2 )

On simplifying,

= ( 2x * 16y^2 ) / ( 3x * 25y^2 )

Cancelling same variables,

= ( 2 * 16 ) / ( 3 * 25 )
= 32 / 75
= ( 2 * 2 * 2 * 2 * 2 ) / ( 5 * 5 * 3 )

Hence we see here that the numerator and denominator have no common number and the ratio is in its simplest form.

= 32 / 75
= 32 : 75

The required answer = 32 : 75

$<marquee>$
$\large\underline\bold{\longrightarrow Thank~You! \longleftarrow}$

Answer 2

Answer:

please search in Google, browser or chrome .thank you.