Question

A solid cylinder is kept on one edge of a plank of same mass and length 25 m placed on a smooth surface as shown in the figure. The coefficient of friction between the cylinder and the plank is 0.5. The plank is given an initial velocity of 20 m/s towards right. Find the time (in sec) after which plank and cylinder will separate.($g=10m/s^2$)

• A. 2

Answer 1

$fr=\mu mg=maa=5m.s^{2}frR=\frac{m{R}^2}{2}\alpha R\alpha =10m/s^2$
Now; t=t sec. when rolling will start [Considering length of planck is sufficient ]
$at+R\alpha t=90-at(2a+R\alpha )t=90T=\frac{20}{20}=1sec$
Now in 1 sec relative displacement of cylinder
$=20\times 1-\frac{1}{2}\times 10\times 1=15m.$
At t= 1 sec rolling will start. Centre of cylinder will move speed 5m/s. Planck will move with speed 15m/s. So extra time taken $\Rightarrow 10=10t^1$
$t^1=1sec$
Total time=1+1=2 sec