Question

If an object completed 49 revolution in a minute around a circular path with speed 7 ms find radius

Answer 1

circumference of the circular path is 2πr where r is the radius.
$speed \: \: s = \frac{d}{t} \\ d = 49 \times 2\pi \: r \\ t = 60s \\ s = 7m {s}^{ - 1} \\ ie. \: 7 = \frac{49 \times 2 \times \frac{22}{7} \times r }{60} \\ r = \frac{7 \times 60 \times 7}{49 \times 2 \times 22} \\ = \frac{15}{11} m$
ie. 1.36 m

Answer 2

The correct answer to the question is 1.364 m.

CALCULATION:

As per the question, the object is taking 49 revolutions per minute.

Hence, the number of rotations taken by the object in one second = $\frac{49}{60}$

The number of rotations made by a body per second is known as the frequency of the body.

Hence, the frequency of the body f = $\frac{49}{60}\ sec^{-1}$ .

The angular velocity of the body $\omega=\ 2\pi f$

                                                             $=\ 2\pi \times \frac{49}{60}\ rad/sec.$

                                                             $=\ 5.13\ rad/sec.$

The velocity of the body v =  7 m/s.

We know that linear velocity v = $\omega r$

                                          ⇒    $r=\ \frac{v}{\omega}$

                                                    $=\ \frac{7}{5.13}\ m$

                                                    $=\ 1.364\ m$     [ans]