Question

A weightless thread can bear tension upto $3.7kg$ wt. A stone of mass $500gm$ is tied to it and revolved in a circular path of radius $4m$ in a vertical plane. If $g=10m{s}^{-2}$, then the maximum angular velocity of the stone will be:

• A. $16rad/s$
• B. $\sqrt{21}rad/s$
• C. $2rad/s$
• D. $4rad/s$

Answer 1

The correct option is D $4rad/s$

Given : $T_{max}=3.7kgwt=37$ N $m=500$ gm $=0.5kg$ $r=4$ m $g=10m/s^2$

Tension in the string is maximum when the stone is at the lowest position of the vertical motion.

Let the maximum angular velocity be $w_{max}$.

Using circular motion equation : $mr{w}_{max}^2=T_{max}-mg$

$\therefore$ $0.5\times 4\times w_{max}^2=37-0.5\times 10$

OR $w_{max}^2=16$ $⟹w_{max}=4$ $rad/s$