What would be the torque about the origin when a force \(3\hat{j}~\text N\) acts on a particle whose position vector is \(2\hat{k}~\text m?\)
Question 2.
A solid cylinder of mass \(2~\text{kg}\) and radius \(4~\text{cm}\) is rotating about its axis at the rate of \(3~\text{rpm}.\) The torque required to stop after \(2\pi\) revolutions is:
Question 3.
The moment of the force, \(\overset{\rightarrow}{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}\) at point (\(2,\)\(0,\)\(-3\)) about the point (\(2,\)\(-2,\)\(-2\)) is given by:
Question 4.
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:
Question 5.
A rod of weight \(w\) is supported by two parallel knife edges, \(A\) and \(B\) , and is in equilibrium in a horizontal position. The knives are at a distance \(d\) from each other. The centre of mass of the rod is at a distance \(x \) from \(A\) . The normal reaction on \(A\) is:
Question 6.
A rod \(PQ\) of mass \(M\) and length \(L\) is hinged at end \(P\). The rod is kept horizontal by a massless string tied to point \(Q\) as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:
Question 7.
\(\mathrm{ABC}\) is an equilateral triangle with \(O\) as its centre. \(F_1,\)\(F_2,\) and \(F_3\) represent three forces acting along the sides \({AB},\)\({BC}\) and \({AC}\) respectively. If the total torque about \(O\) is zero, then the magnitude of \(F_3\) is:
Question 8.
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:
Question 9.
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 \(\frac{Ml^2}{3}\))
Question 10.
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:
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