પાતળી પોલો નળાકાર બંનેને છેડેથી ખુલ્લો છે. તે | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Given: a thin hollow cylinder open at both ends slides without rotating and then rolls without slipping with the same speed.

To find the ratio of k

Vedclass · Accepted Answer

$1 : 2$

Vedclass · Answer

Given: a thin hollow cylinder open at both ends slides without rotating and then rolls without slipping with the same speed.

To find the ratio of kinetic energies in the two cases

Solution:

When hollow cylinder slides without rolling, it posses only transnational

Kinetic energy

$K _{ r }=\frac{1}{2} mv ^2$

When it rolls slipping, it posses both type of Kinetic energy

$K _{ N }=\frac{1}{2} mv ^2\left[1+\frac{ K ^2}{ R ^2}\right]$

Therefore

$\frac{ K _{ r }}{ K _{ N }}=\frac{\frac{1}{2} mv ^2}{\frac{1}{2} mv ^2\left[1+\frac{ K ^2}{ R ^2}\right]}$

and for hollow cylinder $\frac{ K ^2}{ R ^2}=1$

So the above equation becomes,

$\Rightarrow \frac{ K _{ r }}{ K _{ N }}=\frac{1}{2}$

Similar Questions

$3 \;kg $ દળ અને $ 0.2 \;m$ ત્રિજયાનો એક ઘન ગોળો $7\; m$ ઊંચાઇ એક ઢળતા પાટિયા પરથી ગબડે, તો ચાકગતિઊર્જા ($J$ માં) કેટલી થાય?