A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u . Now if it rolls up vertically , the maximum height it would attain will be

A sphere of mass m and radius r rolls on a horizontal plane without sl

1.	A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u . Now if it rolls up vertically , the maximum height it would attain will be
Answer» `3u^(2) //4 g` `5u^(2) //2g` `7u^(2) // 10g ` `U^(2)//2g` SOLUTION :The rolling sphere has rotational as well as TRANSLATIONAL kinetic energy . `therefore` Kinetic energy = `(1)/(2) "mu"^(2) + (1)/(2) I OMEGA^(2)` `= (1)/(2)"mu"^(2) + (1)/(2) ((2)/(5) mr^(2)) omega^(2) = (1)/(2) "mu"^(2) + ("mu"^(2))/(5) = (7)/(10) "mu"^(2)` . Potential energy = kineti energy `therefore mgh = (7)/(10) "mu"^(2) or h = (7u^(2))/(10 g)`