Question

A phonograph record on turn table rotates at $30rpm$. The linear speed of a point on the record at the needle at the beginning of the recording, when it is at a distance of $14cm$ from the centre is

• A. 22 cm / sec
• B. 44 cm / sec
• C. 48 cm / sec
• D. 52 cm / sec

Answer 1

Answer: (B)

44 cm / sec

The linear speed of a point situated at a distance is given by
linear speed = radius x angular velocity
The frequency $=30$ rpm $=30/60=0.5$ rotation per second
Now the angular velocity is given by
$\omega =2\pi f$
$=2$ x $\pi$ x $0.5$
$=\pi rad/s$
So linear speed$=14$ cm x $\pi$
$=14$ x $\frac{22}{7}$ $=44cm/s$