Question

find out the ratio of translational kinetic energy and total kinetic energy of solid cylinder rolling on the plane?​

Answer 1

$\huge{\bold{Heya\:Dost}}$

_________________❤

The ratio of translational kinetic energy and Rotational kinetic energy of solid cylinder rolling on the plane is 1:2

Answer 2

Answer:ANSWER

The rotational kinetic energy is given by

R  

E

​  

=  

2

1

​  

Iω  

2

 

The transnational kinetic energy is given by

T  

E

​  

=  

2

1

​  

Mv  

2

 

Now,

T  

E

​  

 

R  

E

​  

 

​  

=  

2

1

​  

Mv  

2

 

2

1

​  

Iω  

2

 

​  

 

T  

E

​  

 

R  

E

​  

 

​  

=  

v  

2

 

Iω  

2

 

​  

 

Since, I=  

2

1

​  

MR  

2

 ........given

Hence,

T  

E

​  

 

R  

E

​  

 

​  

=  

Mv  

2

 

(  

2

1

​  

MR  

2

)ω  

2

 

​  

 

using, ω=  

R

v

​  

 in above equation, we get

T  

E

​  

 

R  

E

​  

 

​  

=  

v  

2

 

(  

2

1

​  

R  

2

)(  

R

v

​  

)  

2

 

​  

 

T  

E

​  

 

R  

E

​  

 

​  

=  

2

1

​

Explanation:

ANSWER

The rotational kinetic energy is given by

R  

E

​  

=  

2

1

​  

Iω  

2

 

The transnational kinetic energy is given by

T  

E

​  

=  

2

1

​  

Mv  

2

 

Now,

T  

E

​  

 

R  

E

​  

 

​  

=  

2

1

​  

Mv  

2

 

2

1

​  

Iω  

2

 

​  

 

T  

E

​  

 

R  

E

​  

 

​  

=  

v  

2

 

Iω  

2

 

​  

 

Since, I=  

2

1

​  

MR  

2

 ........given

Hence,

T  

E

​  

 

R  

E

​  

 

​  

=  

Mv  

2

 

(  

2

1

​  

MR  

2

)ω  

2

 

​  

 

using, ω=  

R

v

​  

 in above equation, we get

T  

E

​  

 

R  

E

​  

 

​  

=  

v  

2

 

(  

2

1

​  

R  

2

)(  

R

v

​  

)  

2

 

​  

 

T  

E

​  

 

R  

E

​  

 

​  

=  

2

1

​