Question

a solid body rotates about a fixed axis such that its angular velocity depends onθ as = kθ-1where k is a positive constant . at t=0,θ=0, then time dependence ofθ is given as 1)θ = kt 2)θ = 2kt 3)θ = (kt)1/2 4)θ = (2kt)1/2

Answer 1

The time dependence of θ is given as option 4) θ = (2kt)^1/2

Explanation :

Given that, the angular velocity

ω = k/θ

=> dθ/dt = k/θ

=>  θ dθ = k dt

integrating both sides we get

=> θ²/2 = kt + c

putting the initial value t = 0 ,θ = 0 in the equation we get

0 = k x 0 + c

=> c = 0

Hence the equation becomes;

θ²/2 = kt

=> θ² = 2kt

=> θ = (2kt)^1/2

Hence the time dependence of θ is given as option 4) θ = (2kt)^1/2

Answer 2

Answer:The time dependence of θ is given as option 4) θ = (2kt)^1/2

Explanation :

Given that, the angular velocity

ω = k/θ

=> dθ/dt = k/θ

=>  θ dθ = k dt

integrating both sides we get

=> θ²/2 = kt + c

putting the initial value t = 0 ,θ = 0 in the equation we get

0 = k x 0 + c

=> c = 0

Hence the equation becomes;

θ²/2 = kt

=> θ² = 2kt

=> θ = (2kt)^1/2

Hence the time dependence of θ is given as option 4) θ = (2kt)^1/2