Question

A 1000 kg car has four 10 kg wheels. When the car is moving, fraction of total K.E. of the car due to rotation of the wheels about their axles is nearly (Assume wheels be uniform disc)

Options

• `1/50`

• `2/50`

• `3/50`

• `1/100`

Answer 1

`1/50`

Explanation:

K.E. = `4 xx 1/2` Iω² = 2Iω²

T.E. = `1/2` Mv² + `4 xx 1/2` Iω² = `1/2` Mv² + 2Iω²

∴ `(K.E.)/(T.E.) = (2Iω^2)/((1/2 Mv^2 + 2Iω^2))`

= `1/((1 + 1/4  (Mv^2)/(Iω^2))`

= `1/((1 + 2/4  (Mv^2)/(4  mr^2ω^2))`

= `1/((1 + 1/2 M/m)`  ......(∵ v = rω)

= `1/((1 + 1/2 xx 1000/10)) ≈ 1/50`