When a ceiling fan is switched on,it makes 10 | vedclass

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(C) For an object starting from rest with uniform angular acceleration $\alpha$,the angular displacement $	heta$ in time $t$ is given by $	heta = \f

Vedclass · Accepted Answer

$30$

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(C) For an object starting from rest with uniform angular acceleration $\alpha$,the angular displacement $	heta$ in time $t$ is given by $	heta = \frac{1}{2}\alpha t^2$.Since the number of rotations $n$ is proportional to the angular displacement,$n \propto t^2$.Let $n_1$ be the rotations in the first interval $t_1 = 3\,s$,and $n_2$ be the rotations in the next interval $t_2 = 3\,s$.The total rotations in time $2t$ is $n_{total} = n_1 + n_2$.Using the property of uniform acceleration starting from rest,the ratio of rotations in successive equal time intervals is $1 : 3 : 5 : \dots$.Therefore,$n_1 : n_2 = 1 : 3$.Given $n_1 = 10$,we have $10 : n_2 = 1 : 3$.Thus,$n_2 = 10 	imes 3 = 30$ rotations.

When a ceiling fan is switched on,it makes $10$ rotations in the first $3\,s$. How many rotations will it make in the next $3\,s$? (Assume uniform angular acceleration)

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