A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_(t)) as well as rotational kinetic energy (K_(r )) simultaneously. The ratio K_(t):(K_(t)+K_(r )) for the sphere is

A solid sphere is in rolling motion. In rolling motion a body possesse

1.	A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_(t)) as well as rotational kinetic energy (K_(r )) simultaneously. The ratio K_(t):(K_(t)+K_(r )) for the sphere is
Answer» `2:5` `7:10` `10:7` `5:7` SOLUTION :`("Linear KINETIC energy")/("Total kinetic energy")=("Linear kinetic energy")/("ROTATIONAL K.E. + Linear K.E.")` `(K_(t))/(K_(t)+K_(R))=((1)/(2)mv^(2))/((1)/(2)Iomega^(2)+(1)/(2)mv^(2))` `=((1)/(2)mv^(2))/((1)/(2)xx(2)/(5)mr^(2)xx(v^(2))/(r^(2))+(1)/(2)mv^(2))[becauseI=(2)/(5)mr^(2)andv=romega]` `=((1)/(2)mv^(2))/((1)/(5)mv^(2)+(1)/(2)mv^(2))` `=((1)/(2))/((1)/(5)+(1)/(2))` `=((1)/(2))/((7)/(10))=(5)/(7)`