Question

A pulley of radius 1.5 m is rotated about its axis by a force F = (12t – 3t²) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg m², the number of rotations made by the pulley before its direction of motion is reversed, will be K/π. The value of K is ________.

Answer 1

Correct Answer: 18

The correct answer is 18

Fig.

_{I =} 4.5 kg m²
\(FR=Iα\)
\(α=\frac{(12t–3t^2)×1.5}{4.5}=4t−t^2\)
\(w=∫αdt=2t^2–\frac{t^3}{3} \)
w=0
\(⇒t^2(2–\frac{t}{3})0 \)
t=6 sec
\(θ=∫_{0}^{6}[2^t2–\frac{t^3}{3}]dt=[\frac{2t^3}{3}–\frac{t^4}{12}]_{0}^{6}\)
\(=[\frac{2}{3}×6^3–\frac{6^4}{12}]=36\)
\(n=\frac{36}{2π}\)
\(=\frac{18}{π}\)