Question

A uniform solid hemisphere of radius 10 m and mass 64 kg is placed with its curved surface on the smooth horizontal surface and a string AB of length 4 m is attached to point A on its rim as shown in the figure. Find the tension in the string if the hemisphere is in equilibrium.

• A. 320 N
• B. 640 N
• C. 180 N
• D. 360 N

Answer 1

The correct option is C 180 N


$AB=CD=4mThus,OC=6m\sin \left(\theta \right)=\frac{OC}{OA}=\frac{6}{10}\Rightarrow \theta =37°\tan \left(37°\right)=\frac{OC}{BD}=\frac{6}{BD}\Rightarrow BD=8m$

Taking moment about D,

$T\times BD=mg\frac{3}{8}R\sin \left(37°\right)T\times 8=640\times \frac{3}{8}\times 10\times \frac{3}{5}\Rightarrow T=180N$