06. Rolling Motion
Rotational Motion

150400 If rotational inertia parameter of a body rolling down a rough inclined plane (of inclination \(\theta\) and height \(h\)without slipping is given by \(\beta=\) \(\mathrm{I}_{\mathrm{cm}} / \mathrm{MR}^{2}\), then time taken by the body to reach the bottom of the inclined plane is given by

1 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
2 \(\mathrm{t}=\frac{1}{\cos \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
3 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1-\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) \mathrm{h}}{\mathrm{g}}}\)
Rotational Motion

150401 A rigid body of mass \(M\) and radius \(R\) rolls without slipping on an inclined plane of inclination \(\theta\) under gravity. Match the type of body Column I with magnitude of the force of friction Column II.
Column I Column II.

1 A B C D
IV III II I
2 A B C D
I II III IV
3 A B C D
II I IV III
4 A B C D
II IV I III
Rotational Motion

150402 A solid cylinder rolls without slipping from top of an incline of length \(2.7 \mathrm{~m}\) with angle of inclination \(30^{\circ}\). What will be its speed when it reaches the bottom of the incline?
[use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
3 \(3 \mathrm{~m} / \mathrm{s}\)
4 \(3 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150403 If a ring rolls down from top to bottom of an inclined plane, it takes time \(t_{1}\). If it slides, it takes time \(t_{2}\). Then the ratio \(\frac{t_{2}^{2}}{t_{1}^{2}}\) is

1 \(1 / 3\)
2 \(2 / 3\)
3 \(1 / 4\)
4 \(1 / 2\)
5 \(2 / 5\)
Rotational Motion

150400 If rotational inertia parameter of a body rolling down a rough inclined plane (of inclination \(\theta\) and height \(h\)without slipping is given by \(\beta=\) \(\mathrm{I}_{\mathrm{cm}} / \mathrm{MR}^{2}\), then time taken by the body to reach the bottom of the inclined plane is given by

1 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
2 \(\mathrm{t}=\frac{1}{\cos \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
3 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1-\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) \mathrm{h}}{\mathrm{g}}}\)
Rotational Motion

150401 A rigid body of mass \(M\) and radius \(R\) rolls without slipping on an inclined plane of inclination \(\theta\) under gravity. Match the type of body Column I with magnitude of the force of friction Column II.
Column I Column II.

1 A B C D
IV III II I
2 A B C D
I II III IV
3 A B C D
II I IV III
4 A B C D
II IV I III
Rotational Motion

150402 A solid cylinder rolls without slipping from top of an incline of length \(2.7 \mathrm{~m}\) with angle of inclination \(30^{\circ}\). What will be its speed when it reaches the bottom of the incline?
[use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
3 \(3 \mathrm{~m} / \mathrm{s}\)
4 \(3 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150403 If a ring rolls down from top to bottom of an inclined plane, it takes time \(t_{1}\). If it slides, it takes time \(t_{2}\). Then the ratio \(\frac{t_{2}^{2}}{t_{1}^{2}}\) is

1 \(1 / 3\)
2 \(2 / 3\)
3 \(1 / 4\)
4 \(1 / 2\)
5 \(2 / 5\)
Rotational Motion

150400 If rotational inertia parameter of a body rolling down a rough inclined plane (of inclination \(\theta\) and height \(h\)without slipping is given by \(\beta=\) \(\mathrm{I}_{\mathrm{cm}} / \mathrm{MR}^{2}\), then time taken by the body to reach the bottom of the inclined plane is given by

1 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
2 \(\mathrm{t}=\frac{1}{\cos \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
3 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1-\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) \mathrm{h}}{\mathrm{g}}}\)
Rotational Motion

150401 A rigid body of mass \(M\) and radius \(R\) rolls without slipping on an inclined plane of inclination \(\theta\) under gravity. Match the type of body Column I with magnitude of the force of friction Column II.
Column I Column II.

1 A B C D
IV III II I
2 A B C D
I II III IV
3 A B C D
II I IV III
4 A B C D
II IV I III
Rotational Motion

150402 A solid cylinder rolls without slipping from top of an incline of length \(2.7 \mathrm{~m}\) with angle of inclination \(30^{\circ}\). What will be its speed when it reaches the bottom of the incline?
[use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
3 \(3 \mathrm{~m} / \mathrm{s}\)
4 \(3 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150403 If a ring rolls down from top to bottom of an inclined plane, it takes time \(t_{1}\). If it slides, it takes time \(t_{2}\). Then the ratio \(\frac{t_{2}^{2}}{t_{1}^{2}}\) is

1 \(1 / 3\)
2 \(2 / 3\)
3 \(1 / 4\)
4 \(1 / 2\)
5 \(2 / 5\)
Rotational Motion

150400 If rotational inertia parameter of a body rolling down a rough inclined plane (of inclination \(\theta\) and height \(h\)without slipping is given by \(\beta=\) \(\mathrm{I}_{\mathrm{cm}} / \mathrm{MR}^{2}\), then time taken by the body to reach the bottom of the inclined plane is given by

1 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
2 \(\mathrm{t}=\frac{1}{\cos \theta} \sqrt{\frac{(1+\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
3 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1-\beta) 2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{(1+\beta) \mathrm{h}}{\mathrm{g}}}\)
Rotational Motion

150401 A rigid body of mass \(M\) and radius \(R\) rolls without slipping on an inclined plane of inclination \(\theta\) under gravity. Match the type of body Column I with magnitude of the force of friction Column II.
Column I Column II.

1 A B C D
IV III II I
2 A B C D
I II III IV
3 A B C D
II I IV III
4 A B C D
II IV I III
Rotational Motion

150402 A solid cylinder rolls without slipping from top of an incline of length \(2.7 \mathrm{~m}\) with angle of inclination \(30^{\circ}\). What will be its speed when it reaches the bottom of the incline?
[use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(2 \mathrm{~m} / \mathrm{s}\)
2 \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
3 \(3 \mathrm{~m} / \mathrm{s}\)
4 \(3 \sqrt{2} \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150403 If a ring rolls down from top to bottom of an inclined plane, it takes time \(t_{1}\). If it slides, it takes time \(t_{2}\). Then the ratio \(\frac{t_{2}^{2}}{t_{1}^{2}}\) is

1 \(1 / 3\)
2 \(2 / 3\)
3 \(1 / 4\)
4 \(1 / 2\)
5 \(2 / 5\)