MOTION IN A VERTICAL CIRCLE
Work, Energy and Power

268734 A body of mass \(m\) is rotated in a vertical circle with help of light string such that velocity of body at a point is equal to critical velocity at that point. If \(T_{1}, T_{2}\) be the tensions in the string when the body is crossing the highest and the lowest positions then the following relation is correct

1 \(\mathrm{T}_{2}-\mathrm{T}_{1}=6 \mathrm{mg}\)
2 \(\mathrm{T}_{2}-\mathrm{T}_{1}=4 \mathrm{mg}\)
3 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=3 \mathrm{mg}\)
4 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=2 \mathrm{mg}\)
Work, Energy and Power

268735 A vehicle is travelling with uniform speed along a concave road of radius of curvature \(19.6 \mathrm{~m}\). At lowest point of concave road if the normal reaction on the vehicle is three times its weight, the speed of vehicle is

1 \(4.9 \mathrm{~m} / \mathrm{s}\)
2 \(9.8 \mathrm{~m} / \mathrm{s}\)
3 \(14.7 \mathrm{~m} / \mathrm{s}\)
4 \(19.6 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268736 A car is travelling along a flyover bridge which is a part of vertical circle of radius \(10 \mathrm{~m}\). At the highest point of it the normal reaction on the car is half of its weight, the speed of car is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(14 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268737 A very small particle rests on the top of a hemisphere of radius \(20 \mathrm{~cm}\). The smallest horizontal velocity to be given to it, if it has to leave the hemisphere without sliding down its surface \(\left(g=9.8 \mathbf{~ m s}^{-2}\right)\) is

1 \(\sqrt{9.8} \mathrm{~m} / \mathrm{s}\)
2 \(\sqrt{4.9} \mathrm{~m} / \mathrm{s}\)
3 \(\sqrt{1.96} \mathrm{~m} / \mathrm{s}\)
4 \(\sqrt{3.92} \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268788 A simple pendulum of length '\(l\) ' carries a bob of mass ' \(m\) '. If the breaking strength of the string is \(2 \mathrm{mg}\), the maximum angular amplitude from the vertical can be

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Work, Energy and Power

268734 A body of mass \(m\) is rotated in a vertical circle with help of light string such that velocity of body at a point is equal to critical velocity at that point. If \(T_{1}, T_{2}\) be the tensions in the string when the body is crossing the highest and the lowest positions then the following relation is correct

1 \(\mathrm{T}_{2}-\mathrm{T}_{1}=6 \mathrm{mg}\)
2 \(\mathrm{T}_{2}-\mathrm{T}_{1}=4 \mathrm{mg}\)
3 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=3 \mathrm{mg}\)
4 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=2 \mathrm{mg}\)
Work, Energy and Power

268735 A vehicle is travelling with uniform speed along a concave road of radius of curvature \(19.6 \mathrm{~m}\). At lowest point of concave road if the normal reaction on the vehicle is three times its weight, the speed of vehicle is

1 \(4.9 \mathrm{~m} / \mathrm{s}\)
2 \(9.8 \mathrm{~m} / \mathrm{s}\)
3 \(14.7 \mathrm{~m} / \mathrm{s}\)
4 \(19.6 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268736 A car is travelling along a flyover bridge which is a part of vertical circle of radius \(10 \mathrm{~m}\). At the highest point of it the normal reaction on the car is half of its weight, the speed of car is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(14 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268737 A very small particle rests on the top of a hemisphere of radius \(20 \mathrm{~cm}\). The smallest horizontal velocity to be given to it, if it has to leave the hemisphere without sliding down its surface \(\left(g=9.8 \mathbf{~ m s}^{-2}\right)\) is

1 \(\sqrt{9.8} \mathrm{~m} / \mathrm{s}\)
2 \(\sqrt{4.9} \mathrm{~m} / \mathrm{s}\)
3 \(\sqrt{1.96} \mathrm{~m} / \mathrm{s}\)
4 \(\sqrt{3.92} \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268788 A simple pendulum of length '\(l\) ' carries a bob of mass ' \(m\) '. If the breaking strength of the string is \(2 \mathrm{mg}\), the maximum angular amplitude from the vertical can be

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Work, Energy and Power

268734 A body of mass \(m\) is rotated in a vertical circle with help of light string such that velocity of body at a point is equal to critical velocity at that point. If \(T_{1}, T_{2}\) be the tensions in the string when the body is crossing the highest and the lowest positions then the following relation is correct

1 \(\mathrm{T}_{2}-\mathrm{T}_{1}=6 \mathrm{mg}\)
2 \(\mathrm{T}_{2}-\mathrm{T}_{1}=4 \mathrm{mg}\)
3 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=3 \mathrm{mg}\)
4 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=2 \mathrm{mg}\)
Work, Energy and Power

268735 A vehicle is travelling with uniform speed along a concave road of radius of curvature \(19.6 \mathrm{~m}\). At lowest point of concave road if the normal reaction on the vehicle is three times its weight, the speed of vehicle is

1 \(4.9 \mathrm{~m} / \mathrm{s}\)
2 \(9.8 \mathrm{~m} / \mathrm{s}\)
3 \(14.7 \mathrm{~m} / \mathrm{s}\)
4 \(19.6 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268736 A car is travelling along a flyover bridge which is a part of vertical circle of radius \(10 \mathrm{~m}\). At the highest point of it the normal reaction on the car is half of its weight, the speed of car is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(14 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268737 A very small particle rests on the top of a hemisphere of radius \(20 \mathrm{~cm}\). The smallest horizontal velocity to be given to it, if it has to leave the hemisphere without sliding down its surface \(\left(g=9.8 \mathbf{~ m s}^{-2}\right)\) is

1 \(\sqrt{9.8} \mathrm{~m} / \mathrm{s}\)
2 \(\sqrt{4.9} \mathrm{~m} / \mathrm{s}\)
3 \(\sqrt{1.96} \mathrm{~m} / \mathrm{s}\)
4 \(\sqrt{3.92} \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268788 A simple pendulum of length '\(l\) ' carries a bob of mass ' \(m\) '. If the breaking strength of the string is \(2 \mathrm{mg}\), the maximum angular amplitude from the vertical can be

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Work, Energy and Power

268734 A body of mass \(m\) is rotated in a vertical circle with help of light string such that velocity of body at a point is equal to critical velocity at that point. If \(T_{1}, T_{2}\) be the tensions in the string when the body is crossing the highest and the lowest positions then the following relation is correct

1 \(\mathrm{T}_{2}-\mathrm{T}_{1}=6 \mathrm{mg}\)
2 \(\mathrm{T}_{2}-\mathrm{T}_{1}=4 \mathrm{mg}\)
3 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=3 \mathrm{mg}\)
4 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=2 \mathrm{mg}\)
Work, Energy and Power

268735 A vehicle is travelling with uniform speed along a concave road of radius of curvature \(19.6 \mathrm{~m}\). At lowest point of concave road if the normal reaction on the vehicle is three times its weight, the speed of vehicle is

1 \(4.9 \mathrm{~m} / \mathrm{s}\)
2 \(9.8 \mathrm{~m} / \mathrm{s}\)
3 \(14.7 \mathrm{~m} / \mathrm{s}\)
4 \(19.6 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268736 A car is travelling along a flyover bridge which is a part of vertical circle of radius \(10 \mathrm{~m}\). At the highest point of it the normal reaction on the car is half of its weight, the speed of car is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(14 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268737 A very small particle rests on the top of a hemisphere of radius \(20 \mathrm{~cm}\). The smallest horizontal velocity to be given to it, if it has to leave the hemisphere without sliding down its surface \(\left(g=9.8 \mathbf{~ m s}^{-2}\right)\) is

1 \(\sqrt{9.8} \mathrm{~m} / \mathrm{s}\)
2 \(\sqrt{4.9} \mathrm{~m} / \mathrm{s}\)
3 \(\sqrt{1.96} \mathrm{~m} / \mathrm{s}\)
4 \(\sqrt{3.92} \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268788 A simple pendulum of length '\(l\) ' carries a bob of mass ' \(m\) '. If the breaking strength of the string is \(2 \mathrm{mg}\), the maximum angular amplitude from the vertical can be

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Work, Energy and Power

268734 A body of mass \(m\) is rotated in a vertical circle with help of light string such that velocity of body at a point is equal to critical velocity at that point. If \(T_{1}, T_{2}\) be the tensions in the string when the body is crossing the highest and the lowest positions then the following relation is correct

1 \(\mathrm{T}_{2}-\mathrm{T}_{1}=6 \mathrm{mg}\)
2 \(\mathrm{T}_{2}-\mathrm{T}_{1}=4 \mathrm{mg}\)
3 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=3 \mathrm{mg}\)
4 \(\mathrm{T}_{2}^{2}-\mathrm{T}_{1}^{1}=2 \mathrm{mg}\)
Work, Energy and Power

268735 A vehicle is travelling with uniform speed along a concave road of radius of curvature \(19.6 \mathrm{~m}\). At lowest point of concave road if the normal reaction on the vehicle is three times its weight, the speed of vehicle is

1 \(4.9 \mathrm{~m} / \mathrm{s}\)
2 \(9.8 \mathrm{~m} / \mathrm{s}\)
3 \(14.7 \mathrm{~m} / \mathrm{s}\)
4 \(19.6 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268736 A car is travelling along a flyover bridge which is a part of vertical circle of radius \(10 \mathrm{~m}\). At the highest point of it the normal reaction on the car is half of its weight, the speed of car is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(14 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268737 A very small particle rests on the top of a hemisphere of radius \(20 \mathrm{~cm}\). The smallest horizontal velocity to be given to it, if it has to leave the hemisphere without sliding down its surface \(\left(g=9.8 \mathbf{~ m s}^{-2}\right)\) is

1 \(\sqrt{9.8} \mathrm{~m} / \mathrm{s}\)
2 \(\sqrt{4.9} \mathrm{~m} / \mathrm{s}\)
3 \(\sqrt{1.96} \mathrm{~m} / \mathrm{s}\)
4 \(\sqrt{3.92} \mathrm{~m} / \mathrm{s}\)
Work, Energy and Power

268788 A simple pendulum of length '\(l\) ' carries a bob of mass ' \(m\) '. If the breaking strength of the string is \(2 \mathrm{mg}\), the maximum angular amplitude from the vertical can be

1 \(0^{\circ}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)