A solid body rotates about a fixed axis such that its angular velocity depends on θ as ω=k θ-1 where k is a positive constants. At t=0, θ=0, then time dependence of θ is given as

Question

A solid body rotates about a fixed axis such that its angular velocity depends on θ as ω=k θ-1 where k is a positive constants. At t=0, θ=0, then time dependence of θ is given as (A) θ=k t (B) θ=2 k t (C) θ=√k t (D) θ=√2 k t

Tardigrade Admin · Accepted Answer

ω=(k/θ) (d θ/d t)=(k/θ) ∫ θ d θ=k ∫ d t (θ2/2)=k t θ=√2 k t

Q. A solid body rotates about a fixed axis such that its angular velocity depends on $θ$ as $ω = k θ^{- 1}$ where $k$ is a positive constants. At $t = 0, θ = 0$ , then time dependence of $θ$ is given as

$θ = k t$

$θ = 2 k t$

$θ = k t$

$θ = 2 k t$

$ω = \frac{k}{θ}$
$\frac{d θ}{d t} = \frac{k}{θ}$
$\int θ d θ = k \int d t$
$\frac{θ ^{2}}{2} = k t$
$θ = 2 k t$

Q. A solid body rotates about a fixed axis such that its angular velocity depends on θ as ω=kθ−1 where k is a positive constants. At t=0,θ=0, then time dependence of θ is given as

θ=kt

θ=2kt

θ=kt​

θ=2kt​

ω=θk​ dtdθ​=θk​ ∫θdθ=k∫dt 2θ2​=kt θ=2kt​

Q. A solid body rotates about a fixed axis such that its angular velocity depends on $θ$ as $ω = k θ^{- 1}$ where $k$ is a positive constants. At $t = 0, θ = 0$ , then time dependence of $θ$ is given as

$θ = k t$

$θ = 2 k t$

$θ = k t$

$θ = 2 k t$

$ω = \frac{k}{θ}$
$\frac{d θ}{d t} = \frac{k}{θ}$
$\int θ d θ = k \int d t$
$\frac{θ ^{2}}{2} = k t$
$θ = 2 k t$