Question

As shown in figure, wheel A of radius r_A = 10 cm is coupled by belt B to wheel C of radius r_C = 25 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s². Time after which wheel C reaches a rotational speed of 100 rpm, assuming the belt does not slip, is nearly –

• A. 4 sec
• B. 8 sec
• C. 12 sec
• D. 16 sec

Answer 1

Answer: (D)

16 sec

Answer 2

a_t = a_A r_A = a_Cr_C

a_C = a_A $\left( \frac{r_{A}}{r_{C}} \right)$ = 1.6 × $\frac{10}{25}$= 0.64 rad/s²

t = $\frac{\omega_{C}}{\alpha_{C}}$ = $\frac{\frac{100 \times 2\pi}{60}}{0.64}$ = 16.35 sec.