MOTION OF A BODY ON THE INCLINED PLANE
Laws of Motion

270281 The minimum force required to start pushing a body up a rough (frictional coefficient\(\mu\) ) inclined plane is \(F_{1}\) while the minimum force needed to prevent it from sliding down is \(F_{2}\). If the inclined plane makes an angle \(\theta\) with the horizontal such that \(\tan \theta=2 \mu\), then the ratio \(\frac{F_{1}}{F_{2}}\) is (AIEEE-2011)

1 4
2 1
3 2
4 3
Laws of Motion

270280 A block slides down a rough inclined plane of slope angle\(\theta\) with a constant velocity. It is then projected up the same plane with an initial velocity \(v\). The distance travelled by the block up the plane before coming to rest is

1 \(\frac{v^{2}}{4 g \sin ?}\)
2 \(\frac{v^{2}}{2 g \sin ?}\)
3 \(\frac{v^{2}}{\text { gsin? }}\)
4 \(\frac{4 g v^{2}}{\sin ?}\)
Laws of Motion

270283 A body is released from the top of a smooth inclined plane of inclination\(\theta\). It reaches the bottom with velocity \(v\). If the angle of inclina- tion is doubled for the same length of the plane, what will be the velocity of the body on reaching the ground

1 \(v\)
2 \(2 v\)
3 \((2 \cos \theta)^{\frac{1}{2}} v\)
4 \((2 \sin \theta)^{\frac{1}{2}} v\)
Laws of Motion

270284 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is\(60^{\circ}\) is (EAM - 2014)

1 \(\frac{1}{\sqrt{2}}\)
2 \(\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{3}\)
Laws of Motion

270285 A smooth block is released from rest on a\(45^{\circ}\) inclined plane and it slides a distance ' \(d\) '. The time taken to slide is \(\mathbf{n}\) times that on a smooth inclined plane. The coefficient of friction (2010E)

1 \(\mu_{k}=1-\frac{1}{n^{2}}\)
2 \(\mu_{k}=\sqrt{1-\frac{1}{n^{2}}}\)
3 \(\mu_{k}=\frac{1}{1-n^{2}}\)
4 \(\mu_{k}=\sqrt{\frac{1}{1-n^{2}}}\)
Laws of Motion

270281 The minimum force required to start pushing a body up a rough (frictional coefficient\(\mu\) ) inclined plane is \(F_{1}\) while the minimum force needed to prevent it from sliding down is \(F_{2}\). If the inclined plane makes an angle \(\theta\) with the horizontal such that \(\tan \theta=2 \mu\), then the ratio \(\frac{F_{1}}{F_{2}}\) is (AIEEE-2011)

1 4
2 1
3 2
4 3
Laws of Motion

270280 A block slides down a rough inclined plane of slope angle\(\theta\) with a constant velocity. It is then projected up the same plane with an initial velocity \(v\). The distance travelled by the block up the plane before coming to rest is

1 \(\frac{v^{2}}{4 g \sin ?}\)
2 \(\frac{v^{2}}{2 g \sin ?}\)
3 \(\frac{v^{2}}{\text { gsin? }}\)
4 \(\frac{4 g v^{2}}{\sin ?}\)
Laws of Motion

270283 A body is released from the top of a smooth inclined plane of inclination\(\theta\). It reaches the bottom with velocity \(v\). If the angle of inclina- tion is doubled for the same length of the plane, what will be the velocity of the body on reaching the ground

1 \(v\)
2 \(2 v\)
3 \((2 \cos \theta)^{\frac{1}{2}} v\)
4 \((2 \sin \theta)^{\frac{1}{2}} v\)
Laws of Motion

270284 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is\(60^{\circ}\) is (EAM - 2014)

1 \(\frac{1}{\sqrt{2}}\)
2 \(\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{3}\)
Laws of Motion

270285 A smooth block is released from rest on a\(45^{\circ}\) inclined plane and it slides a distance ' \(d\) '. The time taken to slide is \(\mathbf{n}\) times that on a smooth inclined plane. The coefficient of friction (2010E)

1 \(\mu_{k}=1-\frac{1}{n^{2}}\)
2 \(\mu_{k}=\sqrt{1-\frac{1}{n^{2}}}\)
3 \(\mu_{k}=\frac{1}{1-n^{2}}\)
4 \(\mu_{k}=\sqrt{\frac{1}{1-n^{2}}}\)
Laws of Motion

270281 The minimum force required to start pushing a body up a rough (frictional coefficient\(\mu\) ) inclined plane is \(F_{1}\) while the minimum force needed to prevent it from sliding down is \(F_{2}\). If the inclined plane makes an angle \(\theta\) with the horizontal such that \(\tan \theta=2 \mu\), then the ratio \(\frac{F_{1}}{F_{2}}\) is (AIEEE-2011)

1 4
2 1
3 2
4 3
Laws of Motion

270280 A block slides down a rough inclined plane of slope angle\(\theta\) with a constant velocity. It is then projected up the same plane with an initial velocity \(v\). The distance travelled by the block up the plane before coming to rest is

1 \(\frac{v^{2}}{4 g \sin ?}\)
2 \(\frac{v^{2}}{2 g \sin ?}\)
3 \(\frac{v^{2}}{\text { gsin? }}\)
4 \(\frac{4 g v^{2}}{\sin ?}\)
Laws of Motion

270283 A body is released from the top of a smooth inclined plane of inclination\(\theta\). It reaches the bottom with velocity \(v\). If the angle of inclina- tion is doubled for the same length of the plane, what will be the velocity of the body on reaching the ground

1 \(v\)
2 \(2 v\)
3 \((2 \cos \theta)^{\frac{1}{2}} v\)
4 \((2 \sin \theta)^{\frac{1}{2}} v\)
Laws of Motion

270284 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is\(60^{\circ}\) is (EAM - 2014)

1 \(\frac{1}{\sqrt{2}}\)
2 \(\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{3}\)
Laws of Motion

270285 A smooth block is released from rest on a\(45^{\circ}\) inclined plane and it slides a distance ' \(d\) '. The time taken to slide is \(\mathbf{n}\) times that on a smooth inclined plane. The coefficient of friction (2010E)

1 \(\mu_{k}=1-\frac{1}{n^{2}}\)
2 \(\mu_{k}=\sqrt{1-\frac{1}{n^{2}}}\)
3 \(\mu_{k}=\frac{1}{1-n^{2}}\)
4 \(\mu_{k}=\sqrt{\frac{1}{1-n^{2}}}\)
Laws of Motion

270281 The minimum force required to start pushing a body up a rough (frictional coefficient\(\mu\) ) inclined plane is \(F_{1}\) while the minimum force needed to prevent it from sliding down is \(F_{2}\). If the inclined plane makes an angle \(\theta\) with the horizontal such that \(\tan \theta=2 \mu\), then the ratio \(\frac{F_{1}}{F_{2}}\) is (AIEEE-2011)

1 4
2 1
3 2
4 3
Laws of Motion

270280 A block slides down a rough inclined plane of slope angle\(\theta\) with a constant velocity. It is then projected up the same plane with an initial velocity \(v\). The distance travelled by the block up the plane before coming to rest is

1 \(\frac{v^{2}}{4 g \sin ?}\)
2 \(\frac{v^{2}}{2 g \sin ?}\)
3 \(\frac{v^{2}}{\text { gsin? }}\)
4 \(\frac{4 g v^{2}}{\sin ?}\)
Laws of Motion

270283 A body is released from the top of a smooth inclined plane of inclination\(\theta\). It reaches the bottom with velocity \(v\). If the angle of inclina- tion is doubled for the same length of the plane, what will be the velocity of the body on reaching the ground

1 \(v\)
2 \(2 v\)
3 \((2 \cos \theta)^{\frac{1}{2}} v\)
4 \((2 \sin \theta)^{\frac{1}{2}} v\)
Laws of Motion

270284 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is\(60^{\circ}\) is (EAM - 2014)

1 \(\frac{1}{\sqrt{2}}\)
2 \(\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{3}\)
Laws of Motion

270285 A smooth block is released from rest on a\(45^{\circ}\) inclined plane and it slides a distance ' \(d\) '. The time taken to slide is \(\mathbf{n}\) times that on a smooth inclined plane. The coefficient of friction (2010E)

1 \(\mu_{k}=1-\frac{1}{n^{2}}\)
2 \(\mu_{k}=\sqrt{1-\frac{1}{n^{2}}}\)
3 \(\mu_{k}=\frac{1}{1-n^{2}}\)
4 \(\mu_{k}=\sqrt{\frac{1}{1-n^{2}}}\)
Laws of Motion

270281 The minimum force required to start pushing a body up a rough (frictional coefficient\(\mu\) ) inclined plane is \(F_{1}\) while the minimum force needed to prevent it from sliding down is \(F_{2}\). If the inclined plane makes an angle \(\theta\) with the horizontal such that \(\tan \theta=2 \mu\), then the ratio \(\frac{F_{1}}{F_{2}}\) is (AIEEE-2011)

1 4
2 1
3 2
4 3
Laws of Motion

270280 A block slides down a rough inclined plane of slope angle\(\theta\) with a constant velocity. It is then projected up the same plane with an initial velocity \(v\). The distance travelled by the block up the plane before coming to rest is

1 \(\frac{v^{2}}{4 g \sin ?}\)
2 \(\frac{v^{2}}{2 g \sin ?}\)
3 \(\frac{v^{2}}{\text { gsin? }}\)
4 \(\frac{4 g v^{2}}{\sin ?}\)
Laws of Motion

270283 A body is released from the top of a smooth inclined plane of inclination\(\theta\). It reaches the bottom with velocity \(v\). If the angle of inclina- tion is doubled for the same length of the plane, what will be the velocity of the body on reaching the ground

1 \(v\)
2 \(2 v\)
3 \((2 \cos \theta)^{\frac{1}{2}} v\)
4 \((2 \sin \theta)^{\frac{1}{2}} v\)
Laws of Motion

270284 The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is\(60^{\circ}\) is (EAM - 2014)

1 \(\frac{1}{\sqrt{2}}\)
2 \(\frac{1}{\sqrt{3}}\)
3 \(\frac{1}{2}\)
4 \(\frac{1}{3}\)
Laws of Motion

270285 A smooth block is released from rest on a\(45^{\circ}\) inclined plane and it slides a distance ' \(d\) '. The time taken to slide is \(\mathbf{n}\) times that on a smooth inclined plane. The coefficient of friction (2010E)

1 \(\mu_{k}=1-\frac{1}{n^{2}}\)
2 \(\mu_{k}=\sqrt{1-\frac{1}{n^{2}}}\)
3 \(\mu_{k}=\frac{1}{1-n^{2}}\)
4 \(\mu_{k}=\sqrt{\frac{1}{1-n^{2}}}\)