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  4. As shown in the figure, wheel A of radius rA=10 cm is coupled by a belt B to the wheel C of radius rC=25 cm . The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad s- 2 . Time after which wheel C reaches a rotational speed of 100 rpm , assuming the belt does not slip, is nearly <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-rfom3zm9li8w.png />

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Q. As shown in the figure, wheel $A$ of radius $r_{A}=10 \, cm$ is coupled by a belt $B$ to the wheel $C$ of radius $r_{C}=25 \, cm$ . The angular speed of wheel $A$ is increased from rest at a constant rate of $1.6 \, rad \, s^{- 2}$ . Time after which wheel $C$ reaches a rotational speed of $100 \, rpm$ , assuming the belt does not slip, is nearly

Question

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

$a_{t}=\alpha _{A} \, r_{A}=\alpha _{C}r_{C}$
$\alpha_C=\alpha_A\left(\frac{r_A}{r_C}\right)=1.6 \times \frac{10}{25}=0.64 \mathrm{rad} / \mathrm{s}^2$
$t=\frac{\omega _{C}}{\alpha _{C}}=\frac{\frac{100 \times 2 \pi }{60}}{0 .64}=\text{16.35 }s$