A singer, during his performance, stands on the edge of a circular turntable, and begins to walk along its edge with a speed of $1.5\ ms^{-1}$ relative to the ground. The turn table is mounted on a frictionless vertical axle. Its radius R = 3m and its moment of inertia about the axle is 150 kg m². It is initially at rest. If the mass of the singer is 75kg, the time taken by the man to complete one revolution is:

Given:
Speed of the singer relative to the ground, $v = 1.5\text{ m s}^{-1}$
Radius of the circular turntable, $R = 3\text{ m}$

The problem asks for the time taken by the singer to complete one revolution. Since the speed of the singer is given relative to the ground, the time taken to complete one revolution relative to the ground can be calculated directly using the circumference of the circular path.

The total distance covered in one revolution is $2\pi R$.

Time taken $T = \dfrac{2\pi R}{v}$

Substituting the given values:
$T = \dfrac{2\pi \times 3}{1.5}$

$T = 4\pi$

$T = 4 \times 3.1416 \approx 12.57\text{ s}$

The mass of the singer and the moment of inertia of the turntable are extraneous information provided as distractors, as the ground speed is already explicitly given.

Answer: $12.57$s