04. Friction, and Inclined Plane Friction Motion
Laws of Motion

146094 An object takes \(\mathbf{n}\) times as much time as to slide down a \(45^{\circ}\) rough inclined plane as it takes to slide down perfectly smooth inclined planned of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

1 \(\left(1-\frac{1}{\mathrm{n}^{2}}\right)\)
2 \(\left(\frac{1}{1-\mathrm{n}^{2}}\right)\)
3 \(\sqrt{1-\frac{1}{\mathrm{n}^{2}}}\)
4 \(\sqrt{1+\frac{1}{\mathrm{n}^{2}}}\)
Laws of Motion

146095 A block of mass \(m\) is in contact with the cart \(C\) as shown in the figure.

The coefficient of static friction between the block and the cart is \(\mu\). The acceleration \(\alpha\) of the cart that will prevent the block from falling satisfies

1 \(\alpha>\frac{m g}{\mu}\)
2 \(\alpha>\frac{\mathrm{g}}{\mu \mathrm{m}}\)
3 \(\alpha \geq \frac{g}{\mu}\)
4 \(\alpha \lt \frac{g}{\mu}\)
Laws of Motion

146097 A body of mass \(m\) slides down along a frictionless inclined plane from height ' \(h\) ' and just completes motion in a vertical circle of radius \(2 \mathrm{~m}\) after reaching the bottom. What is the value of \(h\) ?
[Use \(\mathrm{g}=\mathbf{1 0 \mathrm { m } / \mathrm { s } ^ { 2 }}\) ]

1 \(2 \mathrm{~m}\)
2 \(\frac{5}{2} \mathrm{~m}\)
3 \(5 \mathrm{~m}\)
4 \(10 \mathrm{~m}\)
Laws of Motion

146098 A cyclist is riding with a speed of \(36 \mathrm{~km} / \mathrm{h}\). As he approaches a circular turn on the road of radius 50, he applies brakes and reduces his speed at the constant rate of \(0.5 \mathrm{~m} / \mathrm{s}\) every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively are

1 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
3 \(\sqrt{17} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
4 \(\frac{\sqrt{17}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
Laws of Motion

146099 A block is placed on a parabolic shape ramp given by equation \(y=\frac{x^{2}}{20}\). If the coefficient of static friction \(\left(\mu_{\mathrm{s}}\right)\) is 0.5 . then what is the maximum height above the ground at which the block can be placed without slipping?

1 \(2.5 \mathrm{~m}\)
2 \(1.25 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.25 \mathrm{~m}\)
Laws of Motion

146094 An object takes \(\mathbf{n}\) times as much time as to slide down a \(45^{\circ}\) rough inclined plane as it takes to slide down perfectly smooth inclined planned of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

1 \(\left(1-\frac{1}{\mathrm{n}^{2}}\right)\)
2 \(\left(\frac{1}{1-\mathrm{n}^{2}}\right)\)
3 \(\sqrt{1-\frac{1}{\mathrm{n}^{2}}}\)
4 \(\sqrt{1+\frac{1}{\mathrm{n}^{2}}}\)
Laws of Motion

146095 A block of mass \(m\) is in contact with the cart \(C\) as shown in the figure.

The coefficient of static friction between the block and the cart is \(\mu\). The acceleration \(\alpha\) of the cart that will prevent the block from falling satisfies

1 \(\alpha>\frac{m g}{\mu}\)
2 \(\alpha>\frac{\mathrm{g}}{\mu \mathrm{m}}\)
3 \(\alpha \geq \frac{g}{\mu}\)
4 \(\alpha \lt \frac{g}{\mu}\)
Laws of Motion

146097 A body of mass \(m\) slides down along a frictionless inclined plane from height ' \(h\) ' and just completes motion in a vertical circle of radius \(2 \mathrm{~m}\) after reaching the bottom. What is the value of \(h\) ?
[Use \(\mathrm{g}=\mathbf{1 0 \mathrm { m } / \mathrm { s } ^ { 2 }}\) ]

1 \(2 \mathrm{~m}\)
2 \(\frac{5}{2} \mathrm{~m}\)
3 \(5 \mathrm{~m}\)
4 \(10 \mathrm{~m}\)
Laws of Motion

146098 A cyclist is riding with a speed of \(36 \mathrm{~km} / \mathrm{h}\). As he approaches a circular turn on the road of radius 50, he applies brakes and reduces his speed at the constant rate of \(0.5 \mathrm{~m} / \mathrm{s}\) every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively are

1 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
3 \(\sqrt{17} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
4 \(\frac{\sqrt{17}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
Laws of Motion

146099 A block is placed on a parabolic shape ramp given by equation \(y=\frac{x^{2}}{20}\). If the coefficient of static friction \(\left(\mu_{\mathrm{s}}\right)\) is 0.5 . then what is the maximum height above the ground at which the block can be placed without slipping?

1 \(2.5 \mathrm{~m}\)
2 \(1.25 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.25 \mathrm{~m}\)
Laws of Motion

146094 An object takes \(\mathbf{n}\) times as much time as to slide down a \(45^{\circ}\) rough inclined plane as it takes to slide down perfectly smooth inclined planned of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

1 \(\left(1-\frac{1}{\mathrm{n}^{2}}\right)\)
2 \(\left(\frac{1}{1-\mathrm{n}^{2}}\right)\)
3 \(\sqrt{1-\frac{1}{\mathrm{n}^{2}}}\)
4 \(\sqrt{1+\frac{1}{\mathrm{n}^{2}}}\)
Laws of Motion

146095 A block of mass \(m\) is in contact with the cart \(C\) as shown in the figure.

The coefficient of static friction between the block and the cart is \(\mu\). The acceleration \(\alpha\) of the cart that will prevent the block from falling satisfies

1 \(\alpha>\frac{m g}{\mu}\)
2 \(\alpha>\frac{\mathrm{g}}{\mu \mathrm{m}}\)
3 \(\alpha \geq \frac{g}{\mu}\)
4 \(\alpha \lt \frac{g}{\mu}\)
Laws of Motion

146097 A body of mass \(m\) slides down along a frictionless inclined plane from height ' \(h\) ' and just completes motion in a vertical circle of radius \(2 \mathrm{~m}\) after reaching the bottom. What is the value of \(h\) ?
[Use \(\mathrm{g}=\mathbf{1 0 \mathrm { m } / \mathrm { s } ^ { 2 }}\) ]

1 \(2 \mathrm{~m}\)
2 \(\frac{5}{2} \mathrm{~m}\)
3 \(5 \mathrm{~m}\)
4 \(10 \mathrm{~m}\)
Laws of Motion

146098 A cyclist is riding with a speed of \(36 \mathrm{~km} / \mathrm{h}\). As he approaches a circular turn on the road of radius 50, he applies brakes and reduces his speed at the constant rate of \(0.5 \mathrm{~m} / \mathrm{s}\) every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively are

1 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
3 \(\sqrt{17} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
4 \(\frac{\sqrt{17}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
Laws of Motion

146099 A block is placed on a parabolic shape ramp given by equation \(y=\frac{x^{2}}{20}\). If the coefficient of static friction \(\left(\mu_{\mathrm{s}}\right)\) is 0.5 . then what is the maximum height above the ground at which the block can be placed without slipping?

1 \(2.5 \mathrm{~m}\)
2 \(1.25 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.25 \mathrm{~m}\)
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Laws of Motion

146094 An object takes \(\mathbf{n}\) times as much time as to slide down a \(45^{\circ}\) rough inclined plane as it takes to slide down perfectly smooth inclined planned of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

1 \(\left(1-\frac{1}{\mathrm{n}^{2}}\right)\)
2 \(\left(\frac{1}{1-\mathrm{n}^{2}}\right)\)
3 \(\sqrt{1-\frac{1}{\mathrm{n}^{2}}}\)
4 \(\sqrt{1+\frac{1}{\mathrm{n}^{2}}}\)
Laws of Motion

146095 A block of mass \(m\) is in contact with the cart \(C\) as shown in the figure.

The coefficient of static friction between the block and the cart is \(\mu\). The acceleration \(\alpha\) of the cart that will prevent the block from falling satisfies

1 \(\alpha>\frac{m g}{\mu}\)
2 \(\alpha>\frac{\mathrm{g}}{\mu \mathrm{m}}\)
3 \(\alpha \geq \frac{g}{\mu}\)
4 \(\alpha \lt \frac{g}{\mu}\)
Laws of Motion

146097 A body of mass \(m\) slides down along a frictionless inclined plane from height ' \(h\) ' and just completes motion in a vertical circle of radius \(2 \mathrm{~m}\) after reaching the bottom. What is the value of \(h\) ?
[Use \(\mathrm{g}=\mathbf{1 0 \mathrm { m } / \mathrm { s } ^ { 2 }}\) ]

1 \(2 \mathrm{~m}\)
2 \(\frac{5}{2} \mathrm{~m}\)
3 \(5 \mathrm{~m}\)
4 \(10 \mathrm{~m}\)
Laws of Motion

146098 A cyclist is riding with a speed of \(36 \mathrm{~km} / \mathrm{h}\). As he approaches a circular turn on the road of radius 50, he applies brakes and reduces his speed at the constant rate of \(0.5 \mathrm{~m} / \mathrm{s}\) every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively are

1 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
3 \(\sqrt{17} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
4 \(\frac{\sqrt{17}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
Laws of Motion

146099 A block is placed on a parabolic shape ramp given by equation \(y=\frac{x^{2}}{20}\). If the coefficient of static friction \(\left(\mu_{\mathrm{s}}\right)\) is 0.5 . then what is the maximum height above the ground at which the block can be placed without slipping?

1 \(2.5 \mathrm{~m}\)
2 \(1.25 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.25 \mathrm{~m}\)
Laws of Motion

146094 An object takes \(\mathbf{n}\) times as much time as to slide down a \(45^{\circ}\) rough inclined plane as it takes to slide down perfectly smooth inclined planned of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

1 \(\left(1-\frac{1}{\mathrm{n}^{2}}\right)\)
2 \(\left(\frac{1}{1-\mathrm{n}^{2}}\right)\)
3 \(\sqrt{1-\frac{1}{\mathrm{n}^{2}}}\)
4 \(\sqrt{1+\frac{1}{\mathrm{n}^{2}}}\)
Laws of Motion

146095 A block of mass \(m\) is in contact with the cart \(C\) as shown in the figure.

The coefficient of static friction between the block and the cart is \(\mu\). The acceleration \(\alpha\) of the cart that will prevent the block from falling satisfies

1 \(\alpha>\frac{m g}{\mu}\)
2 \(\alpha>\frac{\mathrm{g}}{\mu \mathrm{m}}\)
3 \(\alpha \geq \frac{g}{\mu}\)
4 \(\alpha \lt \frac{g}{\mu}\)
Laws of Motion

146097 A body of mass \(m\) slides down along a frictionless inclined plane from height ' \(h\) ' and just completes motion in a vertical circle of radius \(2 \mathrm{~m}\) after reaching the bottom. What is the value of \(h\) ?
[Use \(\mathrm{g}=\mathbf{1 0 \mathrm { m } / \mathrm { s } ^ { 2 }}\) ]

1 \(2 \mathrm{~m}\)
2 \(\frac{5}{2} \mathrm{~m}\)
3 \(5 \mathrm{~m}\)
4 \(10 \mathrm{~m}\)
Laws of Motion

146098 A cyclist is riding with a speed of \(36 \mathrm{~km} / \mathrm{h}\). As he approaches a circular turn on the road of radius 50, he applies brakes and reduces his speed at the constant rate of \(0.5 \mathrm{~m} / \mathrm{s}\) every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively are

1 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
3 \(\sqrt{17} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}\left(\frac{1}{4}\right)\)
4 \(\frac{\sqrt{17}}{2} \mathrm{~m} / \mathrm{s}^{2}, \tan ^{-1}(4)\)
Laws of Motion

146099 A block is placed on a parabolic shape ramp given by equation \(y=\frac{x^{2}}{20}\). If the coefficient of static friction \(\left(\mu_{\mathrm{s}}\right)\) is 0.5 . then what is the maximum height above the ground at which the block can be placed without slipping?

1 \(2.5 \mathrm{~m}\)
2 \(1.25 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.25 \mathrm{~m}\)