Which of the following bodies has the largest kinetic energy

Asked by admin @ 02/08/2021 in Physics viewed by 308 People

.44 Which of the following bodies has the largest kinetic energy?

A) Mass 3 M and speed vC) Mass 2M and speed 3vB) Mass 3 M and speed 4 vD) Mass M and speed 4 v

Answered by admin @ 02/08/2021

Answer- The above question is from the chapter 'Work, Power and Energy'.

Concept used: Formula of Kinetic Energy (K.E.) of a body is given by

$\boxed {\bold {K.E. = \dfrac{1}{2} mv^{2}}}$

Here, m = mass of the body

v = velocity/speed of the body

Given question: Which of the following bodies has the largest kinetic energy?

A) Mass 3M and speed v

B) Mass 2M and speed 3v

C) Mass 3M and speed 4v

D) Mass M and speed 4v

Solution: We know that,

$\boxed {\bold {K.E. = \dfrac{1}{2} mv^{2}}}$

A) Mass = 3M

Speed = v

$K.E. = \dfrac{1}{2}. 3Mv^{2}} \\\\K.E. = \dfrac{3}{2} Mv^{2}}}\\\\\bold {K.E. = 1.5Mv^{2}}}$

B) Mass = 2M

Speed = 3v

$K.E. = \dfrac{1}{2} 2M.(3v)^{2}}\\\\K.E. = 9Mv^{2}}$

C) Mass = 3M

Speed = 4v

$K.E. = \dfrac{1}{2}. 3M.(4v)^{2}}\\\\K.E. = 24Mv^{2}}$

D) Mass = M

Speed = 4v

$K.E. = \dfrac{1}{2} M.(4v)^{2}}\\\\K.E. = 8Mv^{2}}$

As 24Mv² is the largest kinetic energy among others, ∴ body with mass 3M and speed 4v has the largest kinetic energy.

∴ C) Mass 3M and speed 4v is the correct option.

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