Question

A mass $2\text{kg}$ supported by a massless string wound around a uniform hollow cylinder of mass $2\text{kg}$ and radius $1\text{m}$. If the string does not slip on the cylinder, then acceleration of mass is -

• A. $7{\text{m/s}}^2$
• B. $5{\text{m/s}}^2$
• C. $10{\text{m/s}}^2$
• D. $8{\text{m/s}}^2$

Answer 1

The correct option is B $5{\text{m/s}}^2$

Let us suppose acceleration of mass is $a$.
According to question -


Applying $\sum F=\text{ma}$ for mass:
$20-T=2a----\left(1\right)$
Applying $\sum \tau =I\alpha$ for hollow cylinder:
$1\times T=2\times 1^2\times \alpha [\because \tau =r_{\perp }F=I\alpha ,I=m{R}^2]$
$\Rightarrow T=2\times \frac{a}{1}[a=\alpha R]$
$\Rightarrow T=2a----\left(2\right)$
On adding (1) and (2)
$20=4a$
$\Rightarrow a=5{\text{m/s}}^2$
Acceleration of the mass is $5{\text{m/s}}^2$.