Question

A bike racer starting from rest is riding with constant angular acceleration on a circular track. The ratio of angular displacement of the cyclist during $5^{th}$ and $7^{th}$ second is given by

• A. $7:9$
• B. $4:5$
• C. $8:10$
• D. $9:13$

Answer 1

The correct option is D $9:13$

For the angular displacement ${\theta }_{n^{th}}$ in the $n^{th}$ second is given by
${\theta }_{n^{th}}={\omega }_0+\frac{\alpha }{2}(2n-1)$, where $\alpha$ is the constant angular acceleration and ${\omega }_0$ is the initial angular velocity.

Here ${\omega }_0=0$ as cyclist starts from rest.
It is asked that the ratio of angular displacement of the cyclist (starting from rest) at $5^{th}$ and $7^{th}$ second is

${\theta }_{5^{th}}=0+\frac{\alpha }{2}\left(2\right(5)-1)$

${\theta }_{7^{th}}=0+\frac{\alpha }{2}\left(2\right(7)-1)$

$\frac{{\theta }_{5^{th}}}{{\theta }_{7^{th}}}=\frac{9}{13}$
Hence option D is the correct answer.