Question

How many revolutions per minute must the apparatus shown in figure make about a vertical axis so that the cord makes an angle of ${45}^o$ with the vertical.

Answer 1

Length of cord is b.

$b=L\sin q=\left(1.414\right)sin45=1m$;

Let R be the distance between the vertical axis and the mass when the

apparatus rotates.

Hence, $R=a+b=0.20+1m=1.2m$.

$\tan \theta =\frac{v^2}{gr}$

$v=\sqrt{\left(gr\tan \theta \right)}=\sqrt{(9.8\times 1.2\times \tan 45)}=3.429m/s$

revolutions per second,

$=\frac{v}{(2\times \pi \times R)}=\frac{3.429}{(2\times \pi \times 1.2)}=0.454785\times 60=27.287rpm$