Friction, and Inclined Plane Friction Motion
LAWS OF MOTION (ADDITIONAL)

372158 A horizontal force just sufficient to move a body of mass \(4 \mathrm{~kg}\) lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is (take, \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m s}^{-\mathbf{2}}\) ).

1 \(6 \mathrm{~ms}^{-2}\)
2 \(8 \mathrm{~ms}^{-2}\)
3 \(2 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
LAWS OF MOTION (ADDITIONAL)

372159 A particle is place at rest inside a hollow hemisphere of radius \(R\). The coefficient of friction between the particle and the hemisphere is \(\mu=\frac{1}{\sqrt{3}}\). The maximum height up to which the particle can remain stationary is

1 \(\frac{R}{2}\)
2 \(\left(1-\frac{\sqrt{3}}{2}\right) \mathrm{R}\)
3 \(\frac{\sqrt{3}}{2} \mathrm{R}\)
4 \(\frac{3 R}{8}\)
LAWS OF MOTION (ADDITIONAL)

372160 A block of mass \(200 \mathrm{~kg}\) is being pulled up by men on an inclined plane at angle of \(45^{\circ}\) as shown. The coefficient of static friction is 0.5 . Each man can only apply a maximum force of \(500 \mathrm{~N}\). Calculate the number of men required for the block to just start moving up the plane

1 10
2 15
3 5
4 3
LAWS OF MOTION (ADDITIONAL)

372161 A small roller coaster starts at point \(A\) with a speed \(u\) on a curved track as shown in the figure.

The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point \(D\) on the track will be

1 \(\left(u^{2}+g h\right)^{\frac{1}{2}}\)
2 \(\left(u^{2}+2 g h\right)^{\frac{1}{2}}\)
3 \(\left(\mathrm{u}^{2}+4 \mathrm{gh}\right)^{\frac{1}{2}}\)
4 \(u\)
LAWS OF MOTION (ADDITIONAL)

372162 What can be the maximum speed of a car on a turn of radius \(28 \mathrm{~m}\) if the coefficient of friction between the tyres and the road is 0.7 ?
(Take \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) and assume no slope is given to the road)

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(21 \mathrm{~m} / \mathrm{s}\)
4 \(28 \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

372158 A horizontal force just sufficient to move a body of mass \(4 \mathrm{~kg}\) lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is (take, \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m s}^{-\mathbf{2}}\) ).

1 \(6 \mathrm{~ms}^{-2}\)
2 \(8 \mathrm{~ms}^{-2}\)
3 \(2 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
LAWS OF MOTION (ADDITIONAL)

372159 A particle is place at rest inside a hollow hemisphere of radius \(R\). The coefficient of friction between the particle and the hemisphere is \(\mu=\frac{1}{\sqrt{3}}\). The maximum height up to which the particle can remain stationary is

1 \(\frac{R}{2}\)
2 \(\left(1-\frac{\sqrt{3}}{2}\right) \mathrm{R}\)
3 \(\frac{\sqrt{3}}{2} \mathrm{R}\)
4 \(\frac{3 R}{8}\)
LAWS OF MOTION (ADDITIONAL)

372160 A block of mass \(200 \mathrm{~kg}\) is being pulled up by men on an inclined plane at angle of \(45^{\circ}\) as shown. The coefficient of static friction is 0.5 . Each man can only apply a maximum force of \(500 \mathrm{~N}\). Calculate the number of men required for the block to just start moving up the plane

1 10
2 15
3 5
4 3
LAWS OF MOTION (ADDITIONAL)

372161 A small roller coaster starts at point \(A\) with a speed \(u\) on a curved track as shown in the figure.

The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point \(D\) on the track will be

1 \(\left(u^{2}+g h\right)^{\frac{1}{2}}\)
2 \(\left(u^{2}+2 g h\right)^{\frac{1}{2}}\)
3 \(\left(\mathrm{u}^{2}+4 \mathrm{gh}\right)^{\frac{1}{2}}\)
4 \(u\)
LAWS OF MOTION (ADDITIONAL)

372162 What can be the maximum speed of a car on a turn of radius \(28 \mathrm{~m}\) if the coefficient of friction between the tyres and the road is 0.7 ?
(Take \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) and assume no slope is given to the road)

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(21 \mathrm{~m} / \mathrm{s}\)
4 \(28 \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

372158 A horizontal force just sufficient to move a body of mass \(4 \mathrm{~kg}\) lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is (take, \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m s}^{-\mathbf{2}}\) ).

1 \(6 \mathrm{~ms}^{-2}\)
2 \(8 \mathrm{~ms}^{-2}\)
3 \(2 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
LAWS OF MOTION (ADDITIONAL)

372159 A particle is place at rest inside a hollow hemisphere of radius \(R\). The coefficient of friction between the particle and the hemisphere is \(\mu=\frac{1}{\sqrt{3}}\). The maximum height up to which the particle can remain stationary is

1 \(\frac{R}{2}\)
2 \(\left(1-\frac{\sqrt{3}}{2}\right) \mathrm{R}\)
3 \(\frac{\sqrt{3}}{2} \mathrm{R}\)
4 \(\frac{3 R}{8}\)
LAWS OF MOTION (ADDITIONAL)

372160 A block of mass \(200 \mathrm{~kg}\) is being pulled up by men on an inclined plane at angle of \(45^{\circ}\) as shown. The coefficient of static friction is 0.5 . Each man can only apply a maximum force of \(500 \mathrm{~N}\). Calculate the number of men required for the block to just start moving up the plane

1 10
2 15
3 5
4 3
LAWS OF MOTION (ADDITIONAL)

372161 A small roller coaster starts at point \(A\) with a speed \(u\) on a curved track as shown in the figure.

The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point \(D\) on the track will be

1 \(\left(u^{2}+g h\right)^{\frac{1}{2}}\)
2 \(\left(u^{2}+2 g h\right)^{\frac{1}{2}}\)
3 \(\left(\mathrm{u}^{2}+4 \mathrm{gh}\right)^{\frac{1}{2}}\)
4 \(u\)
LAWS OF MOTION (ADDITIONAL)

372162 What can be the maximum speed of a car on a turn of radius \(28 \mathrm{~m}\) if the coefficient of friction between the tyres and the road is 0.7 ?
(Take \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) and assume no slope is given to the road)

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(21 \mathrm{~m} / \mathrm{s}\)
4 \(28 \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

372158 A horizontal force just sufficient to move a body of mass \(4 \mathrm{~kg}\) lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is (take, \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m s}^{-\mathbf{2}}\) ).

1 \(6 \mathrm{~ms}^{-2}\)
2 \(8 \mathrm{~ms}^{-2}\)
3 \(2 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
LAWS OF MOTION (ADDITIONAL)

372159 A particle is place at rest inside a hollow hemisphere of radius \(R\). The coefficient of friction between the particle and the hemisphere is \(\mu=\frac{1}{\sqrt{3}}\). The maximum height up to which the particle can remain stationary is

1 \(\frac{R}{2}\)
2 \(\left(1-\frac{\sqrt{3}}{2}\right) \mathrm{R}\)
3 \(\frac{\sqrt{3}}{2} \mathrm{R}\)
4 \(\frac{3 R}{8}\)
LAWS OF MOTION (ADDITIONAL)

372160 A block of mass \(200 \mathrm{~kg}\) is being pulled up by men on an inclined plane at angle of \(45^{\circ}\) as shown. The coefficient of static friction is 0.5 . Each man can only apply a maximum force of \(500 \mathrm{~N}\). Calculate the number of men required for the block to just start moving up the plane

1 10
2 15
3 5
4 3
LAWS OF MOTION (ADDITIONAL)

372161 A small roller coaster starts at point \(A\) with a speed \(u\) on a curved track as shown in the figure.

The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point \(D\) on the track will be

1 \(\left(u^{2}+g h\right)^{\frac{1}{2}}\)
2 \(\left(u^{2}+2 g h\right)^{\frac{1}{2}}\)
3 \(\left(\mathrm{u}^{2}+4 \mathrm{gh}\right)^{\frac{1}{2}}\)
4 \(u\)
LAWS OF MOTION (ADDITIONAL)

372162 What can be the maximum speed of a car on a turn of radius \(28 \mathrm{~m}\) if the coefficient of friction between the tyres and the road is 0.7 ?
(Take \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) and assume no slope is given to the road)

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(21 \mathrm{~m} / \mathrm{s}\)
4 \(28 \mathrm{~m} / \mathrm{s}\)
LAWS OF MOTION (ADDITIONAL)

372158 A horizontal force just sufficient to move a body of mass \(4 \mathrm{~kg}\) lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is (take, \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m s}^{-\mathbf{2}}\) ).

1 \(6 \mathrm{~ms}^{-2}\)
2 \(8 \mathrm{~ms}^{-2}\)
3 \(2 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
LAWS OF MOTION (ADDITIONAL)

372159 A particle is place at rest inside a hollow hemisphere of radius \(R\). The coefficient of friction between the particle and the hemisphere is \(\mu=\frac{1}{\sqrt{3}}\). The maximum height up to which the particle can remain stationary is

1 \(\frac{R}{2}\)
2 \(\left(1-\frac{\sqrt{3}}{2}\right) \mathrm{R}\)
3 \(\frac{\sqrt{3}}{2} \mathrm{R}\)
4 \(\frac{3 R}{8}\)
LAWS OF MOTION (ADDITIONAL)

372160 A block of mass \(200 \mathrm{~kg}\) is being pulled up by men on an inclined plane at angle of \(45^{\circ}\) as shown. The coefficient of static friction is 0.5 . Each man can only apply a maximum force of \(500 \mathrm{~N}\). Calculate the number of men required for the block to just start moving up the plane

1 10
2 15
3 5
4 3
LAWS OF MOTION (ADDITIONAL)

372161 A small roller coaster starts at point \(A\) with a speed \(u\) on a curved track as shown in the figure.

The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point \(D\) on the track will be

1 \(\left(u^{2}+g h\right)^{\frac{1}{2}}\)
2 \(\left(u^{2}+2 g h\right)^{\frac{1}{2}}\)
3 \(\left(\mathrm{u}^{2}+4 \mathrm{gh}\right)^{\frac{1}{2}}\)
4 \(u\)
LAWS OF MOTION (ADDITIONAL)

372162 What can be the maximum speed of a car on a turn of radius \(28 \mathrm{~m}\) if the coefficient of friction between the tyres and the road is 0.7 ?
(Take \(g=10 \mathrm{~m} / \mathrm{s}^{2}\) and assume no slope is given to the road)

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(21 \mathrm{~m} / \mathrm{s}\)
4 \(28 \mathrm{~m} / \mathrm{s}\)