269538
A thin rod of length\(L\) is vertically straight on horizontal floor. This rod falls freely to one side without slipping of its bottom. The linear velocity of centre of rod when its top end touches floor is
1 \(\sqrt{2 g L}\)
2 \(\sqrt{\frac{3 g L}{2}}\)
3 \(\sqrt{3 g L}\)
4 \(\sqrt{\frac{3 g L}{4}}\)
Explanation:
\(\boldsymbol{\omega}=\sqrt{\frac{3 g}{L}} ; \mathrm{v}=r \omega\) and \(r=\frac{L}{2}\)
Rotational Motion
269539
A wheel of radius '\(r\) ' rolls without slipping with a speed \(v\) on a horizontal road. When it is at a point \(A\) on the road, a small lump of mud separates from the wheel at its highest point \(B\) and drops at point \(C\) on the ground. The distance \(A C\) is
269540
A solid cylinder of mass \(m\) rolls without slipping down an inclined plane making an angle \(\theta\) with the horizontal. The frictional force between the cylinder and the incline is
1 \(m g \sin \theta\)
2 \(\frac{m g \sin \theta}{3}\)
3 \(m g \cos \theta\)
4 \(\frac{2 m g \sin \theta}{3}\)
Explanation:
\(f=m g \sin \theta-\frac{k^{2}}{-k^{2}+R^{2}}\) ～
Rotational Motion
269541
A thin metal disc of radius\(0.25 \mathrm{~m}\) and mass \(2 \mathrm{~kg}\) starts from rest and rolls down an inclined plane. If its rotational kinetic energy is \(4 \mathrm{~J}\) at the foot of the inclined plane, then its linear velocity at the same point is
269538
A thin rod of length\(L\) is vertically straight on horizontal floor. This rod falls freely to one side without slipping of its bottom. The linear velocity of centre of rod when its top end touches floor is
1 \(\sqrt{2 g L}\)
2 \(\sqrt{\frac{3 g L}{2}}\)
3 \(\sqrt{3 g L}\)
4 \(\sqrt{\frac{3 g L}{4}}\)
Explanation:
\(\boldsymbol{\omega}=\sqrt{\frac{3 g}{L}} ; \mathrm{v}=r \omega\) and \(r=\frac{L}{2}\)
Rotational Motion
269539
A wheel of radius '\(r\) ' rolls without slipping with a speed \(v\) on a horizontal road. When it is at a point \(A\) on the road, a small lump of mud separates from the wheel at its highest point \(B\) and drops at point \(C\) on the ground. The distance \(A C\) is
269540
A solid cylinder of mass \(m\) rolls without slipping down an inclined plane making an angle \(\theta\) with the horizontal. The frictional force between the cylinder and the incline is
1 \(m g \sin \theta\)
2 \(\frac{m g \sin \theta}{3}\)
3 \(m g \cos \theta\)
4 \(\frac{2 m g \sin \theta}{3}\)
Explanation:
\(f=m g \sin \theta-\frac{k^{2}}{-k^{2}+R^{2}}\) ～
Rotational Motion
269541
A thin metal disc of radius\(0.25 \mathrm{~m}\) and mass \(2 \mathrm{~kg}\) starts from rest and rolls down an inclined plane. If its rotational kinetic energy is \(4 \mathrm{~J}\) at the foot of the inclined plane, then its linear velocity at the same point is
269538
A thin rod of length\(L\) is vertically straight on horizontal floor. This rod falls freely to one side without slipping of its bottom. The linear velocity of centre of rod when its top end touches floor is
1 \(\sqrt{2 g L}\)
2 \(\sqrt{\frac{3 g L}{2}}\)
3 \(\sqrt{3 g L}\)
4 \(\sqrt{\frac{3 g L}{4}}\)
Explanation:
\(\boldsymbol{\omega}=\sqrt{\frac{3 g}{L}} ; \mathrm{v}=r \omega\) and \(r=\frac{L}{2}\)
Rotational Motion
269539
A wheel of radius '\(r\) ' rolls without slipping with a speed \(v\) on a horizontal road. When it is at a point \(A\) on the road, a small lump of mud separates from the wheel at its highest point \(B\) and drops at point \(C\) on the ground. The distance \(A C\) is
269540
A solid cylinder of mass \(m\) rolls without slipping down an inclined plane making an angle \(\theta\) with the horizontal. The frictional force between the cylinder and the incline is
1 \(m g \sin \theta\)
2 \(\frac{m g \sin \theta}{3}\)
3 \(m g \cos \theta\)
4 \(\frac{2 m g \sin \theta}{3}\)
Explanation:
\(f=m g \sin \theta-\frac{k^{2}}{-k^{2}+R^{2}}\) ～
Rotational Motion
269541
A thin metal disc of radius\(0.25 \mathrm{~m}\) and mass \(2 \mathrm{~kg}\) starts from rest and rolls down an inclined plane. If its rotational kinetic energy is \(4 \mathrm{~J}\) at the foot of the inclined plane, then its linear velocity at the same point is
269538
A thin rod of length\(L\) is vertically straight on horizontal floor. This rod falls freely to one side without slipping of its bottom. The linear velocity of centre of rod when its top end touches floor is
1 \(\sqrt{2 g L}\)
2 \(\sqrt{\frac{3 g L}{2}}\)
3 \(\sqrt{3 g L}\)
4 \(\sqrt{\frac{3 g L}{4}}\)
Explanation:
\(\boldsymbol{\omega}=\sqrt{\frac{3 g}{L}} ; \mathrm{v}=r \omega\) and \(r=\frac{L}{2}\)
Rotational Motion
269539
A wheel of radius '\(r\) ' rolls without slipping with a speed \(v\) on a horizontal road. When it is at a point \(A\) on the road, a small lump of mud separates from the wheel at its highest point \(B\) and drops at point \(C\) on the ground. The distance \(A C\) is
269540
A solid cylinder of mass \(m\) rolls without slipping down an inclined plane making an angle \(\theta\) with the horizontal. The frictional force between the cylinder and the incline is
1 \(m g \sin \theta\)
2 \(\frac{m g \sin \theta}{3}\)
3 \(m g \cos \theta\)
4 \(\frac{2 m g \sin \theta}{3}\)
Explanation:
\(f=m g \sin \theta-\frac{k^{2}}{-k^{2}+R^{2}}\) ～
Rotational Motion
269541
A thin metal disc of radius\(0.25 \mathrm{~m}\) and mass \(2 \mathrm{~kg}\) starts from rest and rolls down an inclined plane. If its rotational kinetic energy is \(4 \mathrm{~J}\) at the foot of the inclined plane, then its linear velocity at the same point is
