1. | \(wx \over d\) | 2. | \(wd \over x\) |
3. | \(w(d-x) \over x\) | 4. | \(w(d-x) \over d\) |
An automobile moves on a road with a speed of \(54~\text{kmh}^{-1}.\) The radius of its wheels is \(0.45\) m and the moment of inertia of the wheel about its axis of rotation is \(3~\text{kg-m}^2.\) If the vehicle is brought to rest in \(15\) s, the magnitude of average torque transmitted by its brakes to the wheel is:
1. \(6.66~\text{kg-m}^2\text{s}^{-2}\)
2. \(8.58~\text{kg-m}^2\text{s}^{-2}\)
3. \(10.86~\text{kg-m}^2\text{s}^{-2}\)
4. \(2.86~\text{kg-m}^2\text{s}^{-2}\)
A rod \(\mathrm{PQ}\) of mass \(M\) and length \(L\) is hinged at end \(\mathrm{P}\). The rod is kept horizontal by a massless string tied to point \(\mathrm{Q}\) as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:
1. \(\frac{g}{L}\)
2. \(\frac{2g}{L}\)
3. \(\frac{2g}{3L}\)
4. \(\frac{3g}{2L}\)
\(\mathrm{ABC}\) is an equilateral triangle with \(O\) as its centre. \(F_1\), \(F_2,\) and \(F_3\) represent three forces acting along the sides \(\mathrm{AB},\) \(\mathrm{BC}\) and \(\mathrm{AC}\) respectively. If the total torque about \(O\) is zero, then the magnitude of \(F_3\) is:
1. \(F_1+F_2\)
2. \(F_1-F_2\)
3. \(\frac{F_1+F_2}{2}\)
4. \(2F_1+F_2\)
If \(\vec F\) is the force acting on a particle having position vector \(\vec r\) and \(\vec \tau\) be the torque of this force about the origin, then:
1. | \(\vec r\cdot\vec \tau\neq0\text{ and }\vec F\cdot\vec \tau=0\) |
2. | \(\vec r\cdot\vec \tau>0\text{ and }\vec F\cdot\vec \tau<0\) |
3. | \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau=0\) |
4. | \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0\) |
A uniform rod of length \(l\) and mass \(M\) is free to rotate in a vertical plane about \(A\). The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about \(A\) is \(\frac{Ml^2}{3}\))
1. \(\frac{3g}{2l}\)
2. \(\frac{2l}{3g}\)
3. \(\frac{3g}{2l^2}\)
4. \(\frac{Mg}{2}\)