01. Angular Displacement, Velocity and Acceleration
Rotational Motion

149811 A mass is whirled in a circular path constant angular velocity and its linear velocity is ' \(V\) '. If the string is now halved keeping the angular momentum same, the linear velocity is

1 \(\frac{V}{2}\)
2 \(2 \mathrm{~V}\)
3 \(\mathrm{V}\)
4 \(\mathrm{V} \sqrt{2}\)
Rotational Motion

149814 A particle starting from rest, moves in a circle of radius ' \(r\) '. It attains a velocity of \(v_{0} \mathrm{~m} / \mathrm{s}\) in the \(n^{\text {th }}\) round. Its angular acceleration will be

1 \(\frac{\mathrm{v}_{0}}{\mathrm{n}} \mathrm{rad} / \mathrm{s}^{2}\)
2 \(\frac{\mathrm{v}_{0}^{2}}{2 \pi \mathrm{nr}^{2}} \mathrm{rad} / \mathrm{s}^{2}\)
3 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
4 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149815 A tractor has its rear wheel with radius \(1.0 \mathrm{~m}\) and front wheel of radius \(0.25 \mathrm{~m}\). The rear wheel is rotating at \(100 \mathrm{rev} / \mathrm{min}\). Calculate the angular speed of the front wheel and the distance covered by the tractor in 10 minutes.

1 \(400 \mathrm{rev} / \mathrm{min}, 6.28 \times 10^{3} \mathrm{~m}\)
2 \(300 \mathrm{rev} / \mathrm{min}, 5.17 \times 10^{3} \mathrm{~m}\)
3 \(200 \mathrm{rev} / \mathrm{min}, 3.14 \times 10^{3} \mathrm{~m}\)
4 \(100 \mathrm{rev} / \mathrm{min}, 1.57 \times 10^{3} \mathrm{~m}\)
Rotational Motion

149816 A uniform rod of mass \(0.5 \mathrm{~kg}\) and length \(0.5 \mathrm{~m}\) is suspended at its ends by means of two light inextensible strings so that the rod is horizontal. If one of the strings is cut, then the angular acceleration of the rod is
(Acceleration due to gravity \(=10 \mathbf{~ m s}_{-2}^{-2}\) )

1 \(60 \mathrm{rads}^{-2}\)
2 \(30 \mathrm{rads}^{-2}\)
3 \(15 \mathrm{rads}^{-2}\)
4 \(10 \mathrm{rads}^{-2}\)
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Rotational Motion

149811 A mass is whirled in a circular path constant angular velocity and its linear velocity is ' \(V\) '. If the string is now halved keeping the angular momentum same, the linear velocity is

1 \(\frac{V}{2}\)
2 \(2 \mathrm{~V}\)
3 \(\mathrm{V}\)
4 \(\mathrm{V} \sqrt{2}\)
Rotational Motion

149814 A particle starting from rest, moves in a circle of radius ' \(r\) '. It attains a velocity of \(v_{0} \mathrm{~m} / \mathrm{s}\) in the \(n^{\text {th }}\) round. Its angular acceleration will be

1 \(\frac{\mathrm{v}_{0}}{\mathrm{n}} \mathrm{rad} / \mathrm{s}^{2}\)
2 \(\frac{\mathrm{v}_{0}^{2}}{2 \pi \mathrm{nr}^{2}} \mathrm{rad} / \mathrm{s}^{2}\)
3 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
4 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149815 A tractor has its rear wheel with radius \(1.0 \mathrm{~m}\) and front wheel of radius \(0.25 \mathrm{~m}\). The rear wheel is rotating at \(100 \mathrm{rev} / \mathrm{min}\). Calculate the angular speed of the front wheel and the distance covered by the tractor in 10 minutes.

1 \(400 \mathrm{rev} / \mathrm{min}, 6.28 \times 10^{3} \mathrm{~m}\)
2 \(300 \mathrm{rev} / \mathrm{min}, 5.17 \times 10^{3} \mathrm{~m}\)
3 \(200 \mathrm{rev} / \mathrm{min}, 3.14 \times 10^{3} \mathrm{~m}\)
4 \(100 \mathrm{rev} / \mathrm{min}, 1.57 \times 10^{3} \mathrm{~m}\)
Rotational Motion

149816 A uniform rod of mass \(0.5 \mathrm{~kg}\) and length \(0.5 \mathrm{~m}\) is suspended at its ends by means of two light inextensible strings so that the rod is horizontal. If one of the strings is cut, then the angular acceleration of the rod is
(Acceleration due to gravity \(=10 \mathbf{~ m s}_{-2}^{-2}\) )

1 \(60 \mathrm{rads}^{-2}\)
2 \(30 \mathrm{rads}^{-2}\)
3 \(15 \mathrm{rads}^{-2}\)
4 \(10 \mathrm{rads}^{-2}\)
Rotational Motion

149811 A mass is whirled in a circular path constant angular velocity and its linear velocity is ' \(V\) '. If the string is now halved keeping the angular momentum same, the linear velocity is

1 \(\frac{V}{2}\)
2 \(2 \mathrm{~V}\)
3 \(\mathrm{V}\)
4 \(\mathrm{V} \sqrt{2}\)
Rotational Motion

149814 A particle starting from rest, moves in a circle of radius ' \(r\) '. It attains a velocity of \(v_{0} \mathrm{~m} / \mathrm{s}\) in the \(n^{\text {th }}\) round. Its angular acceleration will be

1 \(\frac{\mathrm{v}_{0}}{\mathrm{n}} \mathrm{rad} / \mathrm{s}^{2}\)
2 \(\frac{\mathrm{v}_{0}^{2}}{2 \pi \mathrm{nr}^{2}} \mathrm{rad} / \mathrm{s}^{2}\)
3 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
4 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149815 A tractor has its rear wheel with radius \(1.0 \mathrm{~m}\) and front wheel of radius \(0.25 \mathrm{~m}\). The rear wheel is rotating at \(100 \mathrm{rev} / \mathrm{min}\). Calculate the angular speed of the front wheel and the distance covered by the tractor in 10 minutes.

1 \(400 \mathrm{rev} / \mathrm{min}, 6.28 \times 10^{3} \mathrm{~m}\)
2 \(300 \mathrm{rev} / \mathrm{min}, 5.17 \times 10^{3} \mathrm{~m}\)
3 \(200 \mathrm{rev} / \mathrm{min}, 3.14 \times 10^{3} \mathrm{~m}\)
4 \(100 \mathrm{rev} / \mathrm{min}, 1.57 \times 10^{3} \mathrm{~m}\)
Rotational Motion

149816 A uniform rod of mass \(0.5 \mathrm{~kg}\) and length \(0.5 \mathrm{~m}\) is suspended at its ends by means of two light inextensible strings so that the rod is horizontal. If one of the strings is cut, then the angular acceleration of the rod is
(Acceleration due to gravity \(=10 \mathbf{~ m s}_{-2}^{-2}\) )

1 \(60 \mathrm{rads}^{-2}\)
2 \(30 \mathrm{rads}^{-2}\)
3 \(15 \mathrm{rads}^{-2}\)
4 \(10 \mathrm{rads}^{-2}\)
Rotational Motion

149811 A mass is whirled in a circular path constant angular velocity and its linear velocity is ' \(V\) '. If the string is now halved keeping the angular momentum same, the linear velocity is

1 \(\frac{V}{2}\)
2 \(2 \mathrm{~V}\)
3 \(\mathrm{V}\)
4 \(\mathrm{V} \sqrt{2}\)
Rotational Motion

149814 A particle starting from rest, moves in a circle of radius ' \(r\) '. It attains a velocity of \(v_{0} \mathrm{~m} / \mathrm{s}\) in the \(n^{\text {th }}\) round. Its angular acceleration will be

1 \(\frac{\mathrm{v}_{0}}{\mathrm{n}} \mathrm{rad} / \mathrm{s}^{2}\)
2 \(\frac{\mathrm{v}_{0}^{2}}{2 \pi \mathrm{nr}^{2}} \mathrm{rad} / \mathrm{s}^{2}\)
3 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
4 \(\frac{\mathrm{v}_{0}^{2}}{4 \pi \mathrm{nr}} \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149815 A tractor has its rear wheel with radius \(1.0 \mathrm{~m}\) and front wheel of radius \(0.25 \mathrm{~m}\). The rear wheel is rotating at \(100 \mathrm{rev} / \mathrm{min}\). Calculate the angular speed of the front wheel and the distance covered by the tractor in 10 minutes.

1 \(400 \mathrm{rev} / \mathrm{min}, 6.28 \times 10^{3} \mathrm{~m}\)
2 \(300 \mathrm{rev} / \mathrm{min}, 5.17 \times 10^{3} \mathrm{~m}\)
3 \(200 \mathrm{rev} / \mathrm{min}, 3.14 \times 10^{3} \mathrm{~m}\)
4 \(100 \mathrm{rev} / \mathrm{min}, 1.57 \times 10^{3} \mathrm{~m}\)
Rotational Motion

149816 A uniform rod of mass \(0.5 \mathrm{~kg}\) and length \(0.5 \mathrm{~m}\) is suspended at its ends by means of two light inextensible strings so that the rod is horizontal. If one of the strings is cut, then the angular acceleration of the rod is
(Acceleration due to gravity \(=10 \mathbf{~ m s}_{-2}^{-2}\) )

1 \(60 \mathrm{rads}^{-2}\)
2 \(30 \mathrm{rads}^{-2}\)
3 \(15 \mathrm{rads}^{-2}\)
4 \(10 \mathrm{rads}^{-2}\)