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Rotational Motion

269476 A cylinder is released from rest from the top of an incline of inclination $θ$ and length ' $^{'}$ '. If the cylinder roles without slipping, its speed at the bottom

1

\sqrt{\frac{4 g l \sin θ}{3}}

2

\sqrt{\frac{3 g l \sin θ}{2}}

3

\sqrt{\frac{4 g l}{3 \sin θ}}

4

\sqrt{\frac{4 g \sin θ}{3 l}}

Explanation:

$v = \sqrt{\frac{2 g l \sin θ}{1 + \frac{k^{2}}{R^{2}}}}$

Rotational Motion

269477 For a body rolling along a level surface, without slipping the translational and rotational kinetic energies are in the ratio 2:1.The body is

1 Hollow sphere

2 solid cylinder

3 Ring

4 Solid sphere

Explanation:

$\frac{\frac{1}{2} m V^{2}}{\frac{1}{2} I ω^{2}} = \frac{2}{1}$

Rotational Motion

269478 A solid sphere and a spherical shell roll down an incline from rest from same height. The ratio of times taken by them is

1

\sqrt{\frac{21}{25}}

2

\frac{21}{25}

3

\sqrt{\frac{25}{21}}

4

\frac{25}{21}

Explanation:

$t = \frac{\sqrt{21 ◻ ◻^{1} + \frac{k^{2}}{R^{2}}]}}{g \sin θ}$

Rotational Motion

269479 When a solid sphere is rolling along level surface the percentage of its total kinetic energy that is translational is

1

29 %

2

71 %

3

60 %

4

40 %

Rotational Motion

269476 A cylinder is released from rest from the top of an incline of inclination $θ$ and length ' $^{'}$ '. If the cylinder roles without slipping, its speed at the bottom

1

\sqrt{\frac{4 g l \sin θ}{3}}

2

\sqrt{\frac{3 g l \sin θ}{2}}

3

\sqrt{\frac{4 g l}{3 \sin θ}}

4

\sqrt{\frac{4 g \sin θ}{3 l}}

Explanation:

$v = \sqrt{\frac{2 g l \sin θ}{1 + \frac{k^{2}}{R^{2}}}}$

Rotational Motion

269477 For a body rolling along a level surface, without slipping the translational and rotational kinetic energies are in the ratio 2:1.The body is

1 Hollow sphere

2 solid cylinder

3 Ring

4 Solid sphere

Explanation:

$\frac{\frac{1}{2} m V^{2}}{\frac{1}{2} I ω^{2}} = \frac{2}{1}$

Rotational Motion

269478 A solid sphere and a spherical shell roll down an incline from rest from same height. The ratio of times taken by them is

1

\sqrt{\frac{21}{25}}

2

\frac{21}{25}

3

\sqrt{\frac{25}{21}}

4

\frac{25}{21}

Explanation:

$t = \frac{\sqrt{21 ◻ ◻^{1} + \frac{k^{2}}{R^{2}}]}}{g \sin θ}$

Rotational Motion

269479 When a solid sphere is rolling along level surface the percentage of its total kinetic energy that is translational is

1

29 %

2

71 %

3

60 %

4

40 %

Rotational Motion

269476 A cylinder is released from rest from the top of an incline of inclination $θ$ and length ' $^{'}$ '. If the cylinder roles without slipping, its speed at the bottom

1

\sqrt{\frac{4 g l \sin θ}{3}}

2

\sqrt{\frac{3 g l \sin θ}{2}}

3

\sqrt{\frac{4 g l}{3 \sin θ}}

4

\sqrt{\frac{4 g \sin θ}{3 l}}

Explanation:

$v = \sqrt{\frac{2 g l \sin θ}{1 + \frac{k^{2}}{R^{2}}}}$

Rotational Motion

269477 For a body rolling along a level surface, without slipping the translational and rotational kinetic energies are in the ratio 2:1.The body is

1 Hollow sphere

2 solid cylinder

3 Ring

4 Solid sphere

Explanation:

$\frac{\frac{1}{2} m V^{2}}{\frac{1}{2} I ω^{2}} = \frac{2}{1}$

Rotational Motion

269478 A solid sphere and a spherical shell roll down an incline from rest from same height. The ratio of times taken by them is

1

\sqrt{\frac{21}{25}}

2

\frac{21}{25}

3

\sqrt{\frac{25}{21}}

4

\frac{25}{21}

Explanation:

$t = \frac{\sqrt{21 ◻ ◻^{1} + \frac{k^{2}}{R^{2}}]}}{g \sin θ}$

Rotational Motion

269479 When a solid sphere is rolling along level surface the percentage of its total kinetic energy that is translational is

1

29 %

2

71 %

3

60 %

4

40 %

Rotational Motion

269476 A cylinder is released from rest from the top of an incline of inclination $θ$ and length ' $^{'}$ '. If the cylinder roles without slipping, its speed at the bottom

1

\sqrt{\frac{4 g l \sin θ}{3}}

2

\sqrt{\frac{3 g l \sin θ}{2}}

3

\sqrt{\frac{4 g l}{3 \sin θ}}

4

\sqrt{\frac{4 g \sin θ}{3 l}}

Explanation:

$v = \sqrt{\frac{2 g l \sin θ}{1 + \frac{k^{2}}{R^{2}}}}$

Rotational Motion

269477 For a body rolling along a level surface, without slipping the translational and rotational kinetic energies are in the ratio 2:1.The body is

1 Hollow sphere

2 solid cylinder

3 Ring

4 Solid sphere

Explanation:

$\frac{\frac{1}{2} m V^{2}}{\frac{1}{2} I ω^{2}} = \frac{2}{1}$

Rotational Motion

269478 A solid sphere and a spherical shell roll down an incline from rest from same height. The ratio of times taken by them is

1

\sqrt{\frac{21}{25}}

2

\frac{21}{25}

3

\sqrt{\frac{25}{21}}

4

\frac{25}{21}

Explanation:

$t = \frac{\sqrt{21 ◻ ◻^{1} + \frac{k^{2}}{R^{2}}]}}{g \sin θ}$

Rotational Motion

269479 When a solid sphere is rolling along level surface the percentage of its total kinetic energy that is translational is

1

29 %

2

71 %

3

60 %

4

40 %

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