Question

The kinetic energy of an objects mass m moving with the velocity of 5ms in 25j what will be is

Answer 1

$\huge\bold{Answer:-}$

$\sf{Kinetic\:energy,\:E_k=}$$\sf\frac{1}{2}mv^2$

$\sf{i.e.}$$\sf{E_k}$$\propto$${mv^2}$

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$\bold{\large{\boxed{\sf{\green{Given:}}}}}$

$\sf{E_k1}$$\sf{=25J\:and\:V_1=5m/s}$

$\bold{\large{\boxed{\sf{\red{If\:velocity\:is\:doubled:}}}}}$

$\sf{i.e.\:V_2=2V_1}$

$\sf{K.E,\:E_k2}$$\propto$$\sf{(V_2)^2)\:or\:E_k2}$$\propto$$\sf{(2V_1)^2\:or\:E_k}$$\propto$$\sf{4V_1^2}$

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$\sf\underline{Thus,}$$\sf\frac{E_k1}{E_k2}$=$\sf\frac{25}{E_k2}$=$\sf\frac{V_1^2}{4V_1^2}$

$\sf{E_k2=25\times4=100J}$

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Similarly if velocity becomes three times, K.E becomes (3)² times or 9 times.

i.e. $\sf{25J\times9=225J}$