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Physics-

General

Easy

Question

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2 blank s e c$ , it rotates through an angle $theta subscript 1 end subscript$ . In the next $2 blank s e c$ , it rotates through an additional angle $theta subscript 2 end subscript$ . The ratio of $theta subscript 2 end subscript blank divided by theta subscript 1 end subscript$ is

1
2
3
5

The correct answer is: 3

Using relation $theta equals omega subscript 0 end subscript t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent$
$theta subscript 1 end subscript equals fraction numerator 1 over denominator 2 end fraction open parentheses alpha close parentheses open parentheses 2 close parentheses to the power of 2 end exponent equals 2 alpha$ (i)
As $omega subscript 0 end subscript equals 0 comma blank t equals 2 blank s e c$
Now using same equation for $t equals 4 blank s e c comma blank omega subscript 0 end subscript equals 0$
$theta subscript 1 end subscript plus theta subscript 2 end subscript equals fraction numerator 1 over denominator 2 end fraction alpha open parentheses 4 close parentheses to the power of 2 end exponent equals 8 alpha$ (ii)
From (i) and (ii), $theta subscript 1 end subscript equals 2 alpha$ and $theta subscript 2 end subscript equals 6 alpha blank therefore fraction numerator theta subscript 2 end subscript over denominator theta subscript 1 end subscript end fraction equals 3$

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