A sphere of mass 50 gm and diameter 2 cm rolls without slipping with a velocfty of 5 cm/s. Calculate the total energy.

A sphere of mass 50 gm and diameter 2 cm rolls without slipping with a

1.	A sphere of mass 50 gm and diameter 2 cm rolls without slipping with a velocfty of 5 cm/s. Calculate the total energy.
Answer» Solution :`m = 50 gm = 0.05 KG` r = 1 cm `=10^(-2) m, v = 5 cm//s = 0.05 m//s` TOTAL energy = TRANSLATIONAL K.E. + Rotational K.E. `=1/2mv^(2) + 1/2l omega^(2)` But, `I = 2/3 mr^(2)` and `omega = v/r` `=1/2 mv^(2) + 1/2 xx 2/5 mr^(2) omega^(2) = 1/2mv^(2) + 1/5 mr^(2) xx v^(2)/r^(2)` `=7/10 mv^(2) = 7/10 xx 0.05 xx (0.05)^(2) =1/2 mv^(2) +1/5 mr^(2) xx v^(2)/r^(2)` `=7/10 mv^(2) = 7/10 xx 0.05 xx (0.05)^(2) = 8.75 xx 10^(-5) J`