The rope shown in figure is wound around a cylinder of mass 4 kg and moment of inertia 0.02 kgm 2 about the cylinder axis. If the cylinder rolls without slipping, then the linear acceleration of its centre of mass is

Question

The rope shown in figure is wound around a cylinder of mass 4 kg and moment of inertia 0.02 kgm 2 about the cylinder axis. If the cylinder rolls without slipping, then the linear acceleration of its centre of mass is (A) 6.7 m / s 2 (B) 10.0 m / s 2 (C) 3.3 m / s 2 (D) none of the above

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/26c396c3ce18e3bd3b9827d9cb37f20c-.png" /> a=r α, m=4 kg 20+f=4 a 20 r-f r=0.02 α ⇒ a =6.7 m / s 2

Q. The rope shown in figure is wound around a cylinder of mass $4 k g$ and moment of inertia $0.02 k g m^{2}$ about the cylinder axis. If the cylinder rolls without slipping, then the linear acceleration of its centre of mass is

$6.7 m / s^{2}$

$10.0 m / s^{2}$

$3.3 m / s^{2}$

none of the above

$a = r α, m = 4 k g$
$20 + f = 4 a$
$20 r - f r = 0.02 α$
$\Rightarrow a = 6.7 m / s^{2}$

Q. The rope shown in figure is wound around a cylinder of mass 4kg and moment of inertia 0.02kgm2 about the cylinder axis. If the cylinder rolls without slipping, then the linear acceleration of its centre of mass is

6.7m/s2

10.0m/s2

3.3m/s2