Answer:
1.28 m
Explanation:
Given;
Radius, r = 1.5 cm = 0.015 m
Time, t = 19 s
Average angular speed = 4.5 rad/s
Consider a point when the tape is moving at a constant velocity along the circumference of the circular reel of radius r. The linear velocity v at this point is given by;
v = rω ----(1)
Where
v is the linear velocity of the circular motion
r is the radius of the reel
ω is the the angular velocity.
At a point the tap undergoes a linear motion before passing round the reel of the cassette. The linear velocity v at this point is given by;
v = L/t ----(2)
where;
v is the velocity of the linear motion
L is the length of the tape (distance covered by the tape)
t is the time taken
Equating equation(1) and equation (2)
L/t = rω
L = rωt
Substituting the given values,
L = 0.015 × 4.5 × 19
L = 1.2825 m
L = 1.28 m
