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Question
A uniform disc of mass 100g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along with a horizontal table with a velocity of 20 cms-1. (take the surface of the table as reference)
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Solution
Mass of the disc = 100 g = 100 x 10-3 kg = `1/10`kg
Velocity of disc = 20 cm s-1 = 20 x 10-2 ms-1 = 0.2 ms-1
r = 5 cm = `5 xx 10^-2 m, omega = v/r = (20 xx 10^-2)/(5 xx 10^-2) = 4`
Energy = `1/2mV^2 + 1/2Iomega^2 = 1/2(mV^2 + Iomega^2),` where I = `1/2mr^2`
= `1/2[1/10 xx 0.2 xx 0.2 + 1/2 xx 1/10 xx 25 xx 1/10^4 xx 16]`
= `1/2[4/1000 + 2/1000] = 1/2[6/1000]`
Energy = `3 xx 10^-3` J
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