Question

Find the ratio of kinetic energies of two bodies having masses in 1:2 ratio and speeds in 1:3 ratio.

Answer 1

Answer:

K.E=  

2

1

​

 

2m

p  

2

 

​

 where p=momentum

2

1

​

p  

2

 

2

​

/m  

2

​

 

2

1

​

p  

2

 

1

​

/m  

1

​

 

​

=(  

p  

2

​

 

p  

1

​

 

​

)  

2

(  

m  

1

​

 

m  

2

​

 

​

)

1

2

​

=(  

2

1

​

)  

2

(  

m  

1

​

 

m  

2

​

 

​

)

m  

2

​

 

m  

1

​

 

​

=1:8

Explanation:

Answer 2

Answer = 1 : 18

$\bf\huge\underline{\underline{ Given :- }}$

• $m_{1} : m_{2} = 1 : 2$

• $v_{1} : v_{2} = 1:3$

$\bf\huge\underline{\underline{ To \: Find:- }}$

• ratio of Kinetic Energy

$\bf\huge\underline{\underline{ Answer :- }}$

• $KE = \frac{1}{2} m v²$

• $KE_{1} = \frac{1}{2} x . x²$

• $KE_{1} = \frac{x³}{2}$

$\rule{10cm}{0.05cm}$

• $KE_{2} = \frac{1}{2} 2x . (3x)²$

• $KE_{2} = \frac{1}{2} 2x . 9x²$

• $KE_{2} = 9x³$

$\rule{10cm}{0.05cm}$

Ratio

• $KE_{1} : KE_{2} = \frac{x³}{2} : 9x³$

• $KE_{1} : KE_{2} = \frac{1}{2} : 9$

• $KE_{1} : KE_{2} = 1 : 18$