05. Motion in Inclined Plane
Motion in One Dimensions

141961 A horizontal force \(F\) is applied to a block of mass \(m\) on a smooth fixed inclined plane of inclination \(\theta\) to the horizontal as shown in the figure. Resultant force on the block up the plane is
original image

1 \(\mathrm{F} \cos \theta-\mathrm{mg} \sin \theta\)
2 \(\mathrm{F} \sin \theta+\mathrm{mg} \cos \theta\)
3 \(\mathrm{F} \sin \theta-\mathrm{mg} \cos \theta\)
4 \(\mathrm{F} \cos \theta+\mathrm{mg} \sin \theta\)
Motion in One Dimensions

141962 A body is slipping from an inclined plane of height \(h\) and length \(\ell\), angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is

1 \(\sqrt{\frac{2 \ell}{\mathrm{g}}}\)
2 \(\sin \theta \sqrt{\frac{2 h}{g}}\)
3 \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
4 \(\sqrt{\frac{2 h}{g}}\)
Motion in One Dimensions

141963 Two wooden blocks are moving on a smooth horizontal surface such that the block having mass \(m\) remains stationary with respect to block of mass \(M\) as shown in the figure below. The magnitude of the applied force \(P\) is
original image

1 \(g \tan \beta\)
2 \(\mathrm{mg} \cos \beta\)
3 \((\mathrm{M}+\mathrm{m}) \operatorname{cosec} \beta\)
4 \((\mathrm{M}+\mathrm{m}) \mathrm{g} \tan \beta\)
Motion in One Dimensions

141964 A particle slides down on a smooth incline of inclination \(30^{\circ}\), fixed in an elevator going up with an acceleration \(2 \mathrm{~m} / \mathrm{s}^{2}\). The box of incline has a length \(4 \mathrm{~m}\). The time taken by the particle to reach the bottom will be
original image

1 \(\frac{8}{3} \sqrt{3} \mathrm{~s}\)
2 \(\frac{9}{8} \sqrt{3} \mathrm{~s}\)
3 \(\frac{4}{3} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
4 \(\frac{3}{4} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
Motion in One Dimensions

141965 A force \(F=75 \mathrm{~N}\) is applied on a block of mass 5 \(\mathrm{kg}\) along the fixed smooth incline as shown in figure. Here gravitational acceleration \(\mathbf{g}=\mathbf{1 0}\) \(\mathbf{m} / \mathbf{s}^{2}\).
The acceleration of the block is
original image

1 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
2 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
3 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
4 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
Motion in One Dimensions

141961 A horizontal force \(F\) is applied to a block of mass \(m\) on a smooth fixed inclined plane of inclination \(\theta\) to the horizontal as shown in the figure. Resultant force on the block up the plane is
original image

1 \(\mathrm{F} \cos \theta-\mathrm{mg} \sin \theta\)
2 \(\mathrm{F} \sin \theta+\mathrm{mg} \cos \theta\)
3 \(\mathrm{F} \sin \theta-\mathrm{mg} \cos \theta\)
4 \(\mathrm{F} \cos \theta+\mathrm{mg} \sin \theta\)
Motion in One Dimensions

141962 A body is slipping from an inclined plane of height \(h\) and length \(\ell\), angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is

1 \(\sqrt{\frac{2 \ell}{\mathrm{g}}}\)
2 \(\sin \theta \sqrt{\frac{2 h}{g}}\)
3 \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
4 \(\sqrt{\frac{2 h}{g}}\)
Motion in One Dimensions

141963 Two wooden blocks are moving on a smooth horizontal surface such that the block having mass \(m\) remains stationary with respect to block of mass \(M\) as shown in the figure below. The magnitude of the applied force \(P\) is
original image

1 \(g \tan \beta\)
2 \(\mathrm{mg} \cos \beta\)
3 \((\mathrm{M}+\mathrm{m}) \operatorname{cosec} \beta\)
4 \((\mathrm{M}+\mathrm{m}) \mathrm{g} \tan \beta\)
Motion in One Dimensions

141964 A particle slides down on a smooth incline of inclination \(30^{\circ}\), fixed in an elevator going up with an acceleration \(2 \mathrm{~m} / \mathrm{s}^{2}\). The box of incline has a length \(4 \mathrm{~m}\). The time taken by the particle to reach the bottom will be
original image

1 \(\frac{8}{3} \sqrt{3} \mathrm{~s}\)
2 \(\frac{9}{8} \sqrt{3} \mathrm{~s}\)
3 \(\frac{4}{3} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
4 \(\frac{3}{4} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
Motion in One Dimensions

141965 A force \(F=75 \mathrm{~N}\) is applied on a block of mass 5 \(\mathrm{kg}\) along the fixed smooth incline as shown in figure. Here gravitational acceleration \(\mathbf{g}=\mathbf{1 0}\) \(\mathbf{m} / \mathbf{s}^{2}\).
The acceleration of the block is
original image

1 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
2 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
3 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
4 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
Motion in One Dimensions

141961 A horizontal force \(F\) is applied to a block of mass \(m\) on a smooth fixed inclined plane of inclination \(\theta\) to the horizontal as shown in the figure. Resultant force on the block up the plane is
original image

1 \(\mathrm{F} \cos \theta-\mathrm{mg} \sin \theta\)
2 \(\mathrm{F} \sin \theta+\mathrm{mg} \cos \theta\)
3 \(\mathrm{F} \sin \theta-\mathrm{mg} \cos \theta\)
4 \(\mathrm{F} \cos \theta+\mathrm{mg} \sin \theta\)
Motion in One Dimensions

141962 A body is slipping from an inclined plane of height \(h\) and length \(\ell\), angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is

1 \(\sqrt{\frac{2 \ell}{\mathrm{g}}}\)
2 \(\sin \theta \sqrt{\frac{2 h}{g}}\)
3 \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
4 \(\sqrt{\frac{2 h}{g}}\)
Motion in One Dimensions

141963 Two wooden blocks are moving on a smooth horizontal surface such that the block having mass \(m\) remains stationary with respect to block of mass \(M\) as shown in the figure below. The magnitude of the applied force \(P\) is
original image

1 \(g \tan \beta\)
2 \(\mathrm{mg} \cos \beta\)
3 \((\mathrm{M}+\mathrm{m}) \operatorname{cosec} \beta\)
4 \((\mathrm{M}+\mathrm{m}) \mathrm{g} \tan \beta\)
Motion in One Dimensions

141964 A particle slides down on a smooth incline of inclination \(30^{\circ}\), fixed in an elevator going up with an acceleration \(2 \mathrm{~m} / \mathrm{s}^{2}\). The box of incline has a length \(4 \mathrm{~m}\). The time taken by the particle to reach the bottom will be
original image

1 \(\frac{8}{3} \sqrt{3} \mathrm{~s}\)
2 \(\frac{9}{8} \sqrt{3} \mathrm{~s}\)
3 \(\frac{4}{3} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
4 \(\frac{3}{4} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
Motion in One Dimensions

141965 A force \(F=75 \mathrm{~N}\) is applied on a block of mass 5 \(\mathrm{kg}\) along the fixed smooth incline as shown in figure. Here gravitational acceleration \(\mathbf{g}=\mathbf{1 0}\) \(\mathbf{m} / \mathbf{s}^{2}\).
The acceleration of the block is
original image

1 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
2 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
3 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
4 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
Motion in One Dimensions

141961 A horizontal force \(F\) is applied to a block of mass \(m\) on a smooth fixed inclined plane of inclination \(\theta\) to the horizontal as shown in the figure. Resultant force on the block up the plane is
original image

1 \(\mathrm{F} \cos \theta-\mathrm{mg} \sin \theta\)
2 \(\mathrm{F} \sin \theta+\mathrm{mg} \cos \theta\)
3 \(\mathrm{F} \sin \theta-\mathrm{mg} \cos \theta\)
4 \(\mathrm{F} \cos \theta+\mathrm{mg} \sin \theta\)
Motion in One Dimensions

141962 A body is slipping from an inclined plane of height \(h\) and length \(\ell\), angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is

1 \(\sqrt{\frac{2 \ell}{\mathrm{g}}}\)
2 \(\sin \theta \sqrt{\frac{2 h}{g}}\)
3 \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
4 \(\sqrt{\frac{2 h}{g}}\)
Motion in One Dimensions

141963 Two wooden blocks are moving on a smooth horizontal surface such that the block having mass \(m\) remains stationary with respect to block of mass \(M\) as shown in the figure below. The magnitude of the applied force \(P\) is
original image

1 \(g \tan \beta\)
2 \(\mathrm{mg} \cos \beta\)
3 \((\mathrm{M}+\mathrm{m}) \operatorname{cosec} \beta\)
4 \((\mathrm{M}+\mathrm{m}) \mathrm{g} \tan \beta\)
Motion in One Dimensions

141964 A particle slides down on a smooth incline of inclination \(30^{\circ}\), fixed in an elevator going up with an acceleration \(2 \mathrm{~m} / \mathrm{s}^{2}\). The box of incline has a length \(4 \mathrm{~m}\). The time taken by the particle to reach the bottom will be
original image

1 \(\frac{8}{3} \sqrt{3} \mathrm{~s}\)
2 \(\frac{9}{8} \sqrt{3} \mathrm{~s}\)
3 \(\frac{4}{3} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
4 \(\frac{3}{4} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
Motion in One Dimensions

141965 A force \(F=75 \mathrm{~N}\) is applied on a block of mass 5 \(\mathrm{kg}\) along the fixed smooth incline as shown in figure. Here gravitational acceleration \(\mathbf{g}=\mathbf{1 0}\) \(\mathbf{m} / \mathbf{s}^{2}\).
The acceleration of the block is
original image

1 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
2 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
3 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
4 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
Motion in One Dimensions

141961 A horizontal force \(F\) is applied to a block of mass \(m\) on a smooth fixed inclined plane of inclination \(\theta\) to the horizontal as shown in the figure. Resultant force on the block up the plane is
original image

1 \(\mathrm{F} \cos \theta-\mathrm{mg} \sin \theta\)
2 \(\mathrm{F} \sin \theta+\mathrm{mg} \cos \theta\)
3 \(\mathrm{F} \sin \theta-\mathrm{mg} \cos \theta\)
4 \(\mathrm{F} \cos \theta+\mathrm{mg} \sin \theta\)
Motion in One Dimensions

141962 A body is slipping from an inclined plane of height \(h\) and length \(\ell\), angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is

1 \(\sqrt{\frac{2 \ell}{\mathrm{g}}}\)
2 \(\sin \theta \sqrt{\frac{2 h}{g}}\)
3 \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
4 \(\sqrt{\frac{2 h}{g}}\)
Motion in One Dimensions

141963 Two wooden blocks are moving on a smooth horizontal surface such that the block having mass \(m\) remains stationary with respect to block of mass \(M\) as shown in the figure below. The magnitude of the applied force \(P\) is
original image

1 \(g \tan \beta\)
2 \(\mathrm{mg} \cos \beta\)
3 \((\mathrm{M}+\mathrm{m}) \operatorname{cosec} \beta\)
4 \((\mathrm{M}+\mathrm{m}) \mathrm{g} \tan \beta\)
Motion in One Dimensions

141964 A particle slides down on a smooth incline of inclination \(30^{\circ}\), fixed in an elevator going up with an acceleration \(2 \mathrm{~m} / \mathrm{s}^{2}\). The box of incline has a length \(4 \mathrm{~m}\). The time taken by the particle to reach the bottom will be
original image

1 \(\frac{8}{3} \sqrt{3} \mathrm{~s}\)
2 \(\frac{9}{8} \sqrt{3} \mathrm{~s}\)
3 \(\frac{4}{3} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
4 \(\frac{3}{4} \sqrt{\frac{\sqrt{3}}{2}} \mathrm{~s}\)
Motion in One Dimensions

141965 A force \(F=75 \mathrm{~N}\) is applied on a block of mass 5 \(\mathrm{kg}\) along the fixed smooth incline as shown in figure. Here gravitational acceleration \(\mathbf{g}=\mathbf{1 0}\) \(\mathbf{m} / \mathbf{s}^{2}\).
The acceleration of the block is
original image

1 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
2 \(10 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline
3 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) downwards the incline
4 \(5 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) upwards the incline