A constant power is supplied to a disc that can rotate freely about a fixed vertical axis. Angular velocity (ω ) of the disc varies with the number of rotations ( n ) made by the disc after starting from rest as ω =knx . Hence x is: (K is a constant)

Question

A constant power is supplied to a disc that can rotate freely about a fixed vertical axis. Angular velocity (ω ) of the disc varies with the number of rotations ( n ) made by the disc after starting from rest as ω =knx . Hence x is: (K is a constant) (A) (1/3) (B) (3/2) (C) (2/3) (D) 2

Tardigrade Admin · Accepted Answer

τ=Iα P=τω P=I α × ω P=Iω 2(d ω /d θ ) ω 2dω propto dθ ⇒ (ω 3/3) propto θ ω × θ 1 / 3 .

Q. A constant power is supplied to a disc that can rotate freely about a fixed vertical axis. Angular velocity $(ω)$ of the disc varies with the number of rotations ( $n$ ) made by the disc after starting from rest as $ω = k n^{x}$ . Hence $x$ is: (K is a constant)

$\frac{1}{3}$

$\frac{3}{2}$

$\frac{2}{3}$

$2$

$τ = I α$
$P = τ ω$
$P = I α \times ω$
$P = I ω^{2} \frac{d ω}{d θ}$
$ω^{2} d ω \propto d θ \Rightarrow \frac{ω ^{3}}{3} \propto θ$
$ω \times θ^{1/3}$ .

Q. A constant power is supplied to a disc that can rotate freely about a fixed vertical axis. Angular velocity (ω) of the disc varies with the number of rotations ( n ) made by the disc after starting from rest as ω=knx . Hence x is: (K is a constant)

31​

23​

32​

2

τ=Iα P=τω P=Iα×ω P=Iω2dθdω​ ω2dω∝dθ⇒3ω3​∝θ ω×θ1/3 .

Q. A constant power is supplied to a disc that can rotate freely about a fixed vertical axis. Angular velocity $(ω)$ of the disc varies with the number of rotations ( $n$ ) made by the disc after starting from rest as $ω = k n^{x}$ . Hence $x$ is: (K is a constant)

$\frac{1}{3}$

$\frac{3}{2}$

$\frac{2}{3}$

$2$

$τ = I α$
$P = τ ω$
$P = I α \times ω$
$P = I ω^{2} \frac{d ω}{d θ}$
$ω^{2} d ω \propto d θ \Rightarrow \frac{ω ^{3}}{3} \propto θ$
$ω \times θ^{1/3}$ .