In the figure given below, \(O\) is the centre of an equilateral triangle \(ABC\) and \(\vec{F_{1}} ,\vec F_{2}, \vec F_{3}\) are three forces acting along the sides \(AB\), \(BC\) and \(AC\). What should be the magnitude of \(\vec{F_{3}}\) so that total torque about \(O\) is zero?
1. \(\left|\vec{F_{3}}\right|= \left|\vec{F_{1}}\right|+\left|\vec{F_{2}}\right|\)
2. \(\left|\vec{F_{3}}\right|= \left|\vec{F_{1}}\right|-\left|\vec{F_{2}}\right|\)
3. \(\left|\vec{F_{3}}\right|= \vec{F_{1}}+2\vec{F_{2}}\)
4. Not possible
A wheel having a moment of inertia of \(2\) kg–m2 about its vertical axis rotates at the rate of \(60\) rpm about the axis. The torque which can stop the wheel's rotation in one minute would be:
1. | \(\dfrac{\pi }{12}\) N-m | 2. | \(\dfrac{\pi }{15}\) N-m |
3. | \(\dfrac{\pi }{18}\) N-m | 4. | \(\dfrac{2\pi }{15}\) N-m |