A rigid body rotates about a fixed axis with variable angular velocity equal to α-β t , at the time t , where α, β are constants. The angle through which it rotates before it stops is

Correct answer: (A) (α^2)/(2 β). ω=α-β t . Comparing with ω=ω_0-α t Initial angular velocity =α Angular'retardation =β ∴ Angle rotated before it stops is (α^2)/(2 β) . [using .ω^2=ω_0^2+2 β θ ]

Q95 / 100 · BITSAT 2024 (Memory Based Paper 3) · Physics

A rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha-\beta t$, at the time $t$, where $\alpha, \beta$ are constants. The angle through which it rotates before it stops is

Correct answer
A
$\frac{\alpha^2}{2 \beta}$
B
$\frac{\alpha^2-\beta^2}{2 \alpha}$
C
$\frac{\alpha^2-\beta^2}{2 \beta}$
D
$\frac{(\alpha-\beta) \alpha}{2}$

Solution

$\omega=\alpha-\beta t$. Comparing with $\omega=\omega_0-\alpha t$ Initial angular velocity $=\alpha$ Angular'retardation $=\beta$ $\therefore$ Angle rotated before it stops is $\frac{\alpha^2}{2 \beta}$. [using $\left.\omega^2=\omega_0^2+2 \beta \theta\right]$

Hence, the correct answer is option: 'A'.

A rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha-\beta t$, at the time $t$, where $\alpha, \beta$ are constants. The angle through which it rotates before it stops is

Solution

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